From d142f2bfdc7b5ff0107ad56bf3db0a8613275e65 Mon Sep 17 00:00:00 2001
From: Santymax98 <132070198+Santymax98@users.noreply.github.com>
Date: Fri, 17 Nov 2023 00:19:58 -0300
Subject: [PATCH 01/13] Update paper.md

---
 joss/paper.md | 12 +++++-------
 1 file changed, 5 insertions(+), 7 deletions(-)

diff --git a/joss/paper.md b/joss/paper.md
index 4a9ad531..a12fd547 100644
--- a/joss/paper.md
+++ b/joss/paper.md
@@ -8,16 +8,14 @@ authors:
     orcid: 0000-0002-7508-999X
     corresponding: true
     affiliation: 1
-  - name: YOUR NAME
-    orcid: 0000-0000-0000-0000
-    affiliation: "2, 3" # must use "" if you have more than one.
+  - name: Santiago Jimenez
+    orcid: 0000-0002-8198-3656
+    affiliation: 2 # must use "" if you have more than one.
 affiliations:
  - name: SESSTIM, Aix Marseille University, Marseille, France
    index: 1
- - name: YOUR FIRST AFFILIATION
+ - name: Federal University of Pernambuco
    index: 2
- - name: YOUR SECOND AFFILIATION
-   index: 3
 date: 16 November 2023
 bibliography: paper.bib
 
@@ -155,4 +153,4 @@ The package is starting to get used in several other places of the ecosystem. Am
 <!-- If you have to Acknowledge some fundings that might be here. I dont think I do.  -->
 
 
-# References
\ No newline at end of file
+# References

From 49bcc950b911965e46216ea024070ecb3b76d110 Mon Sep 17 00:00:00 2001
From: Santymax98 <santymax9807@gmail.com>
Date: Mon, 20 Nov 2023 15:20:39 -0300
Subject: [PATCH 02/13] 	new file:   src/Plotly_functions.jl 	new file:  
 test/test_plotly.jl

---
 src/Plotly_functions.jl | 227 ++++++++++++++++++++++++++++++++++++++++
 test/test_plotly.jl     |  74 +++++++++++++
 2 files changed, 301 insertions(+)
 create mode 100644 src/Plotly_functions.jl
 create mode 100644 test/test_plotly.jl

diff --git a/src/Plotly_functions.jl b/src/Plotly_functions.jl
new file mode 100644
index 00000000..54a8b2bd
--- /dev/null
+++ b/src/Plotly_functions.jl
@@ -0,0 +1,227 @@
+using Plotly, Distributions, Copulas
+
+function plotly_copula(copula, data::AbstractMatrix, function_type::AbstractString; col = "Viridis", title="", xlabel="u", ylabel="v", show_contours = true, scale = true)
+    #Validate the type of function entered
+    validate_function_type(function_type)
+    
+    colors_3D = ["Blackbody", "Bluered", "Blues", "Cividis", "Earth", "Electric", "Greens", "Greys", "Hot", 
+                    "Jet" , "Picnic", "Portland", "Rainbow", "RdBu", "Reds", "Viridis", "YlGnBu", "YlOrRd"]
+    #Check copula length
+    if length(copula) == 2
+        if function_type == "scatter3d"
+            error("Cannot use 'scatter3d' when copula length is 2.")
+        end
+    elseif length(copula) == 3
+        if function_type != "scatter3d"
+            error("You can only use 'scatter3d' when the copula length is 3.")
+        end
+    else
+        error("The copula length must be 2 or 3.")
+    end
+
+    if function_type == "scatter"
+        if col in colors_3D
+            col = "lightblue"
+        end
+        return plotly_scatter(data, col, title, xlabel, ylabel)
+    elseif function_type == "scatter+hist"
+        if col in colors_3D
+            col = "lightblue"
+        end
+        return plotly_scatter_hist(data, col)
+    elseif function_type == "hist2D"
+        if !(col in colors_3D)
+            @warn("The color '$col' is not in Plotly's predefined list. 'YlGnBu' will be used as the default color.")
+            println("Possible predefined colors in Plotly:")
+            println(colors_3D)
+            col = "YlGnBu"
+        end
+        return plot_histogram_2D(data, col, title, xlabel, ylabel)
+    elseif (function_type == "pdf_contours" || function_type == "cdf_contours")
+        if !(col in colors_3D)
+            @warn("The color '$col' is not in Plotly's predefined list. 'Viridis' will be used as the default color.")
+            println("Possible predefined colors in Plotly:")
+            println(colors_3D)
+            col = "Viridis"
+        end
+        return plotly_contours(copula, function_type, col, title, xlabel, ylabel, scale)  
+    elseif function_type == "scatter3d"
+        return plotly_scatter3D(copula, data, col)
+    else
+        #Check if the color is in the predefined list
+        if !(col in colors_3D)
+            @warn("The color '$col' is not in Plotly's predefined list. 'Viridis' will be used as the default color.")
+            println("Possible predefined colors in Plotly:")
+            println(colors_3D)
+            col = "Viridis"
+        end
+        return plotly_surface(copula, function_type, col, title, xlabel, ylabel, show_contours, scale)
+    end
+end
+
+function validate_function_type(function_type)
+    if !(function_type in ["pdf", "cdf", "scatter", "scatter+hist", "hist2D", "pdf_contours", "cdf_contours", "scatter3d"])
+        error("The function must be 'pdf', 'cdf', 'scatter', 'scatter+hist', 'hist2D', 'pdf_contours', 'cdf_contours', 'scatter3d'")
+    end
+end
+
+function plotly_scatter(data, col, title, xlabel, ylabel)
+    scatter_plotly = Plotly.scatter(
+        x=data[1, :],
+        y=data[2, :],
+        mode="markers",
+        marker=attr(color=col, size=3)
+    )
+
+    layout = create_layout(title, xlabel, ylabel)
+    
+    return Plotly.plot(scatter_plotly, layout)
+end
+
+function plotly_scatter_hist(data, col)
+    trace1 = Plotly.scatter(x=data[1, :], y=data[2, :], mode="markers", marker=attr(color=col, size=3))
+    trace2 = Plotly.histogram(x=data[1, :], xaxis="x", yaxis="y2", marker=attr(color="#c7f6d4"))
+    trace3 = Plotly.histogram(y=data[2, :], xaxis="x2", yaxis="y", marker=attr(color="#caacf9"))
+
+    layout = create_scatter_hist_layout()
+    
+    return Plotly.plot([trace1, trace2, trace3], layout)
+end
+
+function plotly_histogram_2D(data, col, title, xlabel, ylabel)
+    layout = create_hist_2D_layout(title, xlabel, ylabel)
+    return Plotly.plot(histogram2d(x=data[1, :], y=data[2, :], colorscale=col),layout)
+end
+
+function plotly_contours(copula, function_type, col, title, xlabel, ylabel, scale)
+    u = range(0, stop=1, length=100)
+    v = range(0, stop=1, length=100)
+    grid = Iterators.product(u, v)
+
+    z_data = [calculate_value(copula, ui, vi, function_type) for (ui, vi) in grid]
+    z_data = reshape(z_data, 100, 100)
+    layout = create_countors_layout(title, xlabel, ylabel)
+    return Plotly.plot(contour(x=u,y=v, z=z_data, colorscale=col, showscale=scale),layout)
+end
+
+function plotly_surface(copula, function_type, col, title, xlabel, ylabel, show_contours, scale)
+    u = range(0, stop=1, length=100)
+    v = range(0, stop=1, length=100)
+    grid = Iterators.product(u, v)
+
+    z_data = [calculate_value(copula, ui, vi, function_type) for (ui, vi) in grid]
+    z_data = reshape(z_data, 100, 100)
+
+    layout = create_surface_layout(title, xlabel, ylabel, show_contours, scale, col, function_type)
+
+    return Plotly.plot(surface(x=u, y=v, z=z_data, contours_z=show_contours, colorscale=col, showscale=scale), layout)
+end
+
+function calculate_value(copula, ui, vi, function_type)
+    if (function_type == "pdf" || function_type == "pdf_contours")
+        return pdf(copula, [ui, vi])
+    elseif (function_type == "cdf" || function_type == "cdf_contours")
+        return cdf(copula, [ui, vi])
+    end
+end
+
+function plotly_scatter3D(copula, data, col)
+    layout = Layout(
+        scene = attr(
+        xaxis_title = "u",
+        yaxis_title = "v",
+        zaxis_title = "w"
+    ))
+    return Plotly.plot(scatter3d(x = data[1, :], y = data[2, :], z = data[3, :],
+    mode = "markers", 
+    marker = attr(size = 3, color = data[3, :], colorscale=col
+    )),layout)
+end
+
+function create_layout(title, xlabel, ylabel)
+    return Plotly.Layout(
+        title=title,
+        xaxis_title=xlabel,
+        yaxis_title=ylabel,
+        plot_bgcolor="white",
+        paper_bgcolor="white",
+        xaxis=create_axis_properties(),
+        yaxis=create_axis_properties()
+    )
+end
+
+function create_scatter_hist_layout()
+    return Plotly.Layout(
+        autosize=false,
+        plot_bgcolor="white",
+        paper_bgcolor="white",
+        xaxis=create_axis_properties(zeroline=false, domain=[0, 0.81]),
+        yaxis=create_axis_properties(zeroline=false, domain=[0, 0.81]),
+        xaxis2=create_axis_properties(zeroline=false, domain=[0.85, 1]),
+        yaxis2=create_axis_properties(zeroline=true, domain=[0.85, 1]),
+        height=600,
+        width=600,
+        bargap=0,
+        showlegend=false
+    )
+end
+
+function create_hist_2D_layout(title, xlabel, ylabel)
+    return Plotly.Layout(
+        title = title,
+        xaxis=attr(title=xlabel, showgrid=false, zeroline=false),
+        yaxis=attr(title=ylabel, showgrid=false, zeroline=false),
+        autosize=false,
+        height=500,
+        width=500,
+        hovermode="closest",
+        showlegend=false
+    )
+end
+
+function create_surface_layout(title, xlabel, ylabel, show_contours, scale, col, function_type)
+    contours_settings = show_contours ? attr(show=true, usecolormap=true, project_z=true, showlines=true) : false
+
+    zaxis_title = function_type == "pdf" ? "PDF" : (function_type == "cdf" ? "CDF" : "function_type")
+
+    return Plotly.Layout(
+        title=title,
+        autosize=false,
+        scene_camera_eye=attr(x=1.87, y=0.88, z=-0.64),
+        width=500,
+        height=500,
+        margin=attr(l=65, r=50, b=65, t=90),
+        scene=attr(xaxis_title=xlabel, yaxis_title=ylabel, zaxis_title=zaxis_title),
+        xaxis=create_axis_properties(),
+        yaxis=create_axis_properties(),
+        showlegend=false
+    )
+end
+
+function create_axis_properties(; zeroline=true, domain=[0, 1], showgrid=true, gridcolor="#FAFAFA", gridwidth=0.5, griddash="solid", showline=true, linecolor="black")
+    return attr(
+        zeroline=zeroline,
+        domain=domain,
+        showgrid=showgrid,
+        gridcolor=gridcolor,
+        gridwidth=gridwidth,
+        griddash=griddash,
+        showline=showline,
+        linecolor=linecolor
+    )
+end
+
+function create_countors_layout(title, xlabel, ylabel)
+  return Plotly.Layout(
+    title = title,
+    xaxis = attr(title = xlabel, showgrid = false, zeroline = false),
+    yaxis = attr(title = ylabel, showgrid = false, zeroline = false),
+    autosize = false,
+    height = 500,
+    width = 500,
+    hovermode = "closest",
+    showlegend = false
+    )
+end
+
+
diff --git a/test/test_plotly.jl b/test/test_plotly.jl
new file mode 100644
index 00000000..4047f705
--- /dev/null
+++ b/test/test_plotly.jl
@@ -0,0 +1,74 @@
+using Test
+# Test function for plotly_copula
+function test_plotly_copula_methods()
+    # Create data and copula for testing
+    X1 = Gamma(2, 3)
+    X2 = Pareto()
+    C = ClaytonCopula(2, 3.5)
+    D = SklarDist(C, (X1, X2))
+    samples = rand(D, 1000)
+    
+    # Methods to try
+    methods = ["pdf", "cdf", "scatter", "scatter+hist", "hist2D", "pdf_contours", "cdf_contours", "scatter3d"]
+    
+    for method in methods
+        println("Testing method: $method")
+        
+        if method == "scatter3d" && length(D) == 2
+            # Test 1: Verify that plotly_copula generates an error for scatter3d with bivariate copula
+            @test_throws ErrorException plotly_copula(D, samples, method)
+        else
+            # Test 1: Verify that plotly_copula does not throw errors
+            result = plotly_copula(D, samples, method)
+            
+           # Test 2: Verify that plotly_copula generates a plot
+           @test isa(result, PlotlyJS.SyncPlot)
+        end
+    end
+end
+
+
+@testset "Graphics Function Tests" begin
+    test_plotly_copula_methods()
+end
+
+# Función de prueba para plotly_copula
+function test_multivariate_copula_methods()
+    # Methods to prove
+    Methods = ["scatter", "scatter+hist", "hist2D", "pdf_contours", "cdf_contours", "pdf", "cdf"]
+    
+    for method in Methods
+        for i in [4, 5,6]
+            D_mult = InvGaussianCopula(i, 2.5)
+            samples_mult = rand(D_mult, 300)
+            println("Testing method for multivariate copula: $method")
+            @test_throws ErrorException plotly_copula(D_mult, samples_mult, method)
+        end
+    end 
+    
+    # Trivariate prove
+    for method in Methods
+        for i in [1, 2, 3]
+            T = JoeCopula(3, i)
+            samples_tri = rand(T, 1000)
+            
+            try
+                if length(T) == 3 && method == "scatter3d"
+                    result = plotly_copula(T, samples_tri, method)
+                    @test isa(result, PlotlyJS.SyncPlot)
+                else
+                    println("Testing method for trivariate copula: $method")
+                    @test_throws ErrorException plotly_copula(T, samples_tri, method)
+                end
+            catch ex
+                println("Error in method $method for trivariate copula: $ex")
+            end
+        end
+    end
+end
+
+# Ejecutar la prueba
+@testset "Tests de funciones de gráficos para copulas multivariadas" begin
+    test_multivariate_copula_methods()
+end
+

From 30fcb75bb674be6032e031bacc563870f68db0eb Mon Sep 17 00:00:00 2001
From: Santymax98 <santymax9807@gmail.com>
Date: Wed, 29 Nov 2023 22:53:20 -0300
Subject: [PATCH 03/13] 	new file:   src/MiscellaneousCopulas/RafteryCopula.jl 
 deleted:    src/Plotly_functions.jl 	new file:   test/RafteryTest.jl 
 deleted:    test/test_plotly.jl

---
 src/MiscellaneousCopulas/RafteryCopula.jl | 106 ++++++++++
 src/Plotly_functions.jl                   | 227 ----------------------
 test/RafteryTest.jl                       |  42 ++++
 test/test_plotly.jl                       |  74 -------
 4 files changed, 148 insertions(+), 301 deletions(-)
 create mode 100644 src/MiscellaneousCopulas/RafteryCopula.jl
 delete mode 100644 src/Plotly_functions.jl
 create mode 100644 test/RafteryTest.jl
 delete mode 100644 test/test_plotly.jl

diff --git a/src/MiscellaneousCopulas/RafteryCopula.jl b/src/MiscellaneousCopulas/RafteryCopula.jl
new file mode 100644
index 00000000..fc1ceb6f
--- /dev/null
+++ b/src/MiscellaneousCopulas/RafteryCopula.jl
@@ -0,0 +1,106 @@
+"""
+    RafteryCopula{d, P}
+
+Fields:
+  - θ::Real - parameter
+
+Constructor
+
+    RafteryCopula(d, θ)
+
+The Multivariate Raftery Copula of dimension d is arameterized by ``\\theta \\in [0,1]`` 
+
+```math
+C_{\\theta}(\\mathbf{u}) = u_{(1)} + \\frac{(1 - \\theta)(1 - d)}{1 - \\theta - d} \\left(\\prod_{j=1}^{d} u_j\\right)^{\\frac{1}{1-\\theta}} - \\sum_{i=2}^{d} \\frac{\\theta(1-\\theta)}{(1-\\theta-i)(2-\\theta-i)} \\left(\\prod_{j=1}^{i-1}u_{(j)}\\right)^{\\frac{1}{1-\\theta}}u_{(i)}^{\\frac{2-\\theta-i}{1-\\theta}}
+```
+
+
+where ``u_{(1)}, \\ldots , u_{(d)}`` denote the order statistics of ``u_1, \\ldots ,u_d``.
+
+More details about Multivariate Raftery Copula are found in :
+
+    Saali, T., M. Mesfioui, and A. Shabri, 2023: Multivariate Extension of Raftery Copula. Mathematics, 11, 414, https://doi.org/10.3390/math11020414.    
+    
+    Nelsen, Roger B. An introduction to copulas. Springer, 2006. Exercise 3.6.
+
+It has a few special cases:
+- When θ = 0, it is the IndependentCopula.
+- When θ = 1, it is the the Fréchet upper bound
+"""
+struct RafteryCopula{d, P} <: Copula{d}
+    θ::P  # Copula parameter
+    function RafteryCopula(d,θ)
+        if (θ < 0) || (θ > 1)
+            throw(ArgumentError("Theta must be in [0,1]"))
+        elseif θ == 0
+            return IndependentCopula(d)
+        elseif θ == 1
+            return MCopula(d)
+        else
+            return new{d,typeof(θ)}(θ)
+        end
+    end
+end
+function _cdf(R::RafteryCopula, u::Vector{T}) where {T}
+    if length(u) != R.d
+        throw(ArgumentError("Dimension mismatch"))
+    end
+    
+    # Order the vector u
+    u_ordered = sort(u)
+    
+    term1 = u_ordered[1]
+    term2 = (1 - R.θ) * (1 - R.d) / (1 - R.θ - R.d) * prod(u).^(1/(1 - R.θ))
+
+    term3 = 0.0
+    for i in 2:R.d
+        prod_prev = prod(u_ordered[1:i-1])
+        term3 += R.θ * (1 - R.θ) / ((1 - R.θ - i) * (2 - R.θ - i)) * prod_prev^(1/(1 - R.θ)) * u_ordered[i]^((2 - R.θ - i) / (1 - R.θ))
+    end
+    # Combine the terms to get the cumulative distribution function
+    cdf_value = term1 + term2 - term3
+    
+    return cdf_value
+end
+
+function Distributions._logpdf(R::RafteryCopula, u::Vector{T}) where {T}
+    if length(u) != R.d
+        throw(ArgumentError("Dimension mismatch"))
+    end
+    
+    # Order the vector u 
+    u_ordered = sort(u)
+    
+    term_denominator = (1 - R.θ)^(R.d - 1) * (1 - R.θ - R.d)
+    term_numerator = 1 - R.d - R.θ * u_ordered[R.d]^((1 - R.θ - R.d) / (1 - R.θ))
+    term_product = prod(u)^((R.θ) / (1 - R.θ))
+    
+    logpdf_value = log(term_numerator) - log(term_denominator) + log(term_product)
+    
+    return logpdf_value
+end
+
+function Distributions._rand!(rng::Distributions.AbstractRNG, R::RafteryCopula{d,P}, x::AbstractVector{T}) where {d,P,T <: Real}
+    
+    dim = length(x)
+    
+    # Paso 1: Generar valores independientes u, u_1, ..., u_d desde una distribución uniforme [0, 1]
+    u = rand(rng, dim+1)
+    
+    # Paso 2: Generar j desde una distribución de Bernoulli con parámetro θ
+    j = rand(Bernoulli(R.θ),1)
+    uj = u[1].^j
+    # Paso 3: Calcular v_1, ..., v_d
+    for i in 2:dim+1
+        x[i] = u[i]^(1 - R.θ) * uj
+    end
+    
+    return x
+end
+
+function ρ(R::RafteryCopula{d,R}) where {d, P}
+    term1 = (d+1)*(2^d-(2-R.θ)^d)-(2^d*R.θ*d)
+    term2 = (2-R.θ)^d*(2^d-d-1) 
+    return term1/term2
+end
+
diff --git a/src/Plotly_functions.jl b/src/Plotly_functions.jl
deleted file mode 100644
index 54a8b2bd..00000000
--- a/src/Plotly_functions.jl
+++ /dev/null
@@ -1,227 +0,0 @@
-using Plotly, Distributions, Copulas
-
-function plotly_copula(copula, data::AbstractMatrix, function_type::AbstractString; col = "Viridis", title="", xlabel="u", ylabel="v", show_contours = true, scale = true)
-    #Validate the type of function entered
-    validate_function_type(function_type)
-    
-    colors_3D = ["Blackbody", "Bluered", "Blues", "Cividis", "Earth", "Electric", "Greens", "Greys", "Hot", 
-                    "Jet" , "Picnic", "Portland", "Rainbow", "RdBu", "Reds", "Viridis", "YlGnBu", "YlOrRd"]
-    #Check copula length
-    if length(copula) == 2
-        if function_type == "scatter3d"
-            error("Cannot use 'scatter3d' when copula length is 2.")
-        end
-    elseif length(copula) == 3
-        if function_type != "scatter3d"
-            error("You can only use 'scatter3d' when the copula length is 3.")
-        end
-    else
-        error("The copula length must be 2 or 3.")
-    end
-
-    if function_type == "scatter"
-        if col in colors_3D
-            col = "lightblue"
-        end
-        return plotly_scatter(data, col, title, xlabel, ylabel)
-    elseif function_type == "scatter+hist"
-        if col in colors_3D
-            col = "lightblue"
-        end
-        return plotly_scatter_hist(data, col)
-    elseif function_type == "hist2D"
-        if !(col in colors_3D)
-            @warn("The color '$col' is not in Plotly's predefined list. 'YlGnBu' will be used as the default color.")
-            println("Possible predefined colors in Plotly:")
-            println(colors_3D)
-            col = "YlGnBu"
-        end
-        return plot_histogram_2D(data, col, title, xlabel, ylabel)
-    elseif (function_type == "pdf_contours" || function_type == "cdf_contours")
-        if !(col in colors_3D)
-            @warn("The color '$col' is not in Plotly's predefined list. 'Viridis' will be used as the default color.")
-            println("Possible predefined colors in Plotly:")
-            println(colors_3D)
-            col = "Viridis"
-        end
-        return plotly_contours(copula, function_type, col, title, xlabel, ylabel, scale)  
-    elseif function_type == "scatter3d"
-        return plotly_scatter3D(copula, data, col)
-    else
-        #Check if the color is in the predefined list
-        if !(col in colors_3D)
-            @warn("The color '$col' is not in Plotly's predefined list. 'Viridis' will be used as the default color.")
-            println("Possible predefined colors in Plotly:")
-            println(colors_3D)
-            col = "Viridis"
-        end
-        return plotly_surface(copula, function_type, col, title, xlabel, ylabel, show_contours, scale)
-    end
-end
-
-function validate_function_type(function_type)
-    if !(function_type in ["pdf", "cdf", "scatter", "scatter+hist", "hist2D", "pdf_contours", "cdf_contours", "scatter3d"])
-        error("The function must be 'pdf', 'cdf', 'scatter', 'scatter+hist', 'hist2D', 'pdf_contours', 'cdf_contours', 'scatter3d'")
-    end
-end
-
-function plotly_scatter(data, col, title, xlabel, ylabel)
-    scatter_plotly = Plotly.scatter(
-        x=data[1, :],
-        y=data[2, :],
-        mode="markers",
-        marker=attr(color=col, size=3)
-    )
-
-    layout = create_layout(title, xlabel, ylabel)
-    
-    return Plotly.plot(scatter_plotly, layout)
-end
-
-function plotly_scatter_hist(data, col)
-    trace1 = Plotly.scatter(x=data[1, :], y=data[2, :], mode="markers", marker=attr(color=col, size=3))
-    trace2 = Plotly.histogram(x=data[1, :], xaxis="x", yaxis="y2", marker=attr(color="#c7f6d4"))
-    trace3 = Plotly.histogram(y=data[2, :], xaxis="x2", yaxis="y", marker=attr(color="#caacf9"))
-
-    layout = create_scatter_hist_layout()
-    
-    return Plotly.plot([trace1, trace2, trace3], layout)
-end
-
-function plotly_histogram_2D(data, col, title, xlabel, ylabel)
-    layout = create_hist_2D_layout(title, xlabel, ylabel)
-    return Plotly.plot(histogram2d(x=data[1, :], y=data[2, :], colorscale=col),layout)
-end
-
-function plotly_contours(copula, function_type, col, title, xlabel, ylabel, scale)
-    u = range(0, stop=1, length=100)
-    v = range(0, stop=1, length=100)
-    grid = Iterators.product(u, v)
-
-    z_data = [calculate_value(copula, ui, vi, function_type) for (ui, vi) in grid]
-    z_data = reshape(z_data, 100, 100)
-    layout = create_countors_layout(title, xlabel, ylabel)
-    return Plotly.plot(contour(x=u,y=v, z=z_data, colorscale=col, showscale=scale),layout)
-end
-
-function plotly_surface(copula, function_type, col, title, xlabel, ylabel, show_contours, scale)
-    u = range(0, stop=1, length=100)
-    v = range(0, stop=1, length=100)
-    grid = Iterators.product(u, v)
-
-    z_data = [calculate_value(copula, ui, vi, function_type) for (ui, vi) in grid]
-    z_data = reshape(z_data, 100, 100)
-
-    layout = create_surface_layout(title, xlabel, ylabel, show_contours, scale, col, function_type)
-
-    return Plotly.plot(surface(x=u, y=v, z=z_data, contours_z=show_contours, colorscale=col, showscale=scale), layout)
-end
-
-function calculate_value(copula, ui, vi, function_type)
-    if (function_type == "pdf" || function_type == "pdf_contours")
-        return pdf(copula, [ui, vi])
-    elseif (function_type == "cdf" || function_type == "cdf_contours")
-        return cdf(copula, [ui, vi])
-    end
-end
-
-function plotly_scatter3D(copula, data, col)
-    layout = Layout(
-        scene = attr(
-        xaxis_title = "u",
-        yaxis_title = "v",
-        zaxis_title = "w"
-    ))
-    return Plotly.plot(scatter3d(x = data[1, :], y = data[2, :], z = data[3, :],
-    mode = "markers", 
-    marker = attr(size = 3, color = data[3, :], colorscale=col
-    )),layout)
-end
-
-function create_layout(title, xlabel, ylabel)
-    return Plotly.Layout(
-        title=title,
-        xaxis_title=xlabel,
-        yaxis_title=ylabel,
-        plot_bgcolor="white",
-        paper_bgcolor="white",
-        xaxis=create_axis_properties(),
-        yaxis=create_axis_properties()
-    )
-end
-
-function create_scatter_hist_layout()
-    return Plotly.Layout(
-        autosize=false,
-        plot_bgcolor="white",
-        paper_bgcolor="white",
-        xaxis=create_axis_properties(zeroline=false, domain=[0, 0.81]),
-        yaxis=create_axis_properties(zeroline=false, domain=[0, 0.81]),
-        xaxis2=create_axis_properties(zeroline=false, domain=[0.85, 1]),
-        yaxis2=create_axis_properties(zeroline=true, domain=[0.85, 1]),
-        height=600,
-        width=600,
-        bargap=0,
-        showlegend=false
-    )
-end
-
-function create_hist_2D_layout(title, xlabel, ylabel)
-    return Plotly.Layout(
-        title = title,
-        xaxis=attr(title=xlabel, showgrid=false, zeroline=false),
-        yaxis=attr(title=ylabel, showgrid=false, zeroline=false),
-        autosize=false,
-        height=500,
-        width=500,
-        hovermode="closest",
-        showlegend=false
-    )
-end
-
-function create_surface_layout(title, xlabel, ylabel, show_contours, scale, col, function_type)
-    contours_settings = show_contours ? attr(show=true, usecolormap=true, project_z=true, showlines=true) : false
-
-    zaxis_title = function_type == "pdf" ? "PDF" : (function_type == "cdf" ? "CDF" : "function_type")
-
-    return Plotly.Layout(
-        title=title,
-        autosize=false,
-        scene_camera_eye=attr(x=1.87, y=0.88, z=-0.64),
-        width=500,
-        height=500,
-        margin=attr(l=65, r=50, b=65, t=90),
-        scene=attr(xaxis_title=xlabel, yaxis_title=ylabel, zaxis_title=zaxis_title),
-        xaxis=create_axis_properties(),
-        yaxis=create_axis_properties(),
-        showlegend=false
-    )
-end
-
-function create_axis_properties(; zeroline=true, domain=[0, 1], showgrid=true, gridcolor="#FAFAFA", gridwidth=0.5, griddash="solid", showline=true, linecolor="black")
-    return attr(
-        zeroline=zeroline,
-        domain=domain,
-        showgrid=showgrid,
-        gridcolor=gridcolor,
-        gridwidth=gridwidth,
-        griddash=griddash,
-        showline=showline,
-        linecolor=linecolor
-    )
-end
-
-function create_countors_layout(title, xlabel, ylabel)
-  return Plotly.Layout(
-    title = title,
-    xaxis = attr(title = xlabel, showgrid = false, zeroline = false),
-    yaxis = attr(title = ylabel, showgrid = false, zeroline = false),
-    autosize = false,
-    height = 500,
-    width = 500,
-    hovermode = "closest",
-    showlegend = false
-    )
-end
-
-
diff --git a/test/RafteryTest.jl b/test/RafteryTest.jl
new file mode 100644
index 00000000..63a567f7
--- /dev/null
+++ b/test/RafteryTest.jl
@@ -0,0 +1,42 @@
+@testitem "RafteryCopula Constructor" begin
+    for d in [2,3,4]
+        @test isa(RarfteryCopula(d,0.0), IndependentCopula)
+        @test isa(RarfteryCopula(d,1.0), MCopula)
+    end    
+    @test_throws ArgumentError RafteryCopula(1,0.5)
+    @test_throws ArgumentError RafteryCopula(3,-1.5)
+    @test_throws ArgumentError RafteryCopula(2, 2.6)
+end
+
+@testset "RafteryCopula CDF" begin
+    
+    for d in [2, 3, 4]
+        F = RafteryCopula(d, 0.5)
+
+        # Test CDF with some random values
+        u = rand(d)
+        cdf_value = cdf(F, u)
+        @test cdf_value >= 0 && cdf_value <= 1
+    end
+end
+
+@testset "RafteryCopula PDF" begin
+    
+    for d in [2, 3, 4]
+        F = RafteryCopula(d, 0.5)
+
+        # Test PDF with some random values
+        u = rand(d)
+        pdf_value = pdf(F, u)
+        @test pdf_value >= 0
+    end
+end
+
+@testitem "RafteryCopula Sampling" begin
+    using StableRNGs
+    rng = StableRNG(123)
+    n_samples = 100
+    F = RafteryCopula(3,0.5)
+    samples = rand(rng,F, n_samples)
+    @test size(samples) == (3, n_samples)
+end
\ No newline at end of file
diff --git a/test/test_plotly.jl b/test/test_plotly.jl
deleted file mode 100644
index 4047f705..00000000
--- a/test/test_plotly.jl
+++ /dev/null
@@ -1,74 +0,0 @@
-using Test
-# Test function for plotly_copula
-function test_plotly_copula_methods()
-    # Create data and copula for testing
-    X1 = Gamma(2, 3)
-    X2 = Pareto()
-    C = ClaytonCopula(2, 3.5)
-    D = SklarDist(C, (X1, X2))
-    samples = rand(D, 1000)
-    
-    # Methods to try
-    methods = ["pdf", "cdf", "scatter", "scatter+hist", "hist2D", "pdf_contours", "cdf_contours", "scatter3d"]
-    
-    for method in methods
-        println("Testing method: $method")
-        
-        if method == "scatter3d" && length(D) == 2
-            # Test 1: Verify that plotly_copula generates an error for scatter3d with bivariate copula
-            @test_throws ErrorException plotly_copula(D, samples, method)
-        else
-            # Test 1: Verify that plotly_copula does not throw errors
-            result = plotly_copula(D, samples, method)
-            
-           # Test 2: Verify that plotly_copula generates a plot
-           @test isa(result, PlotlyJS.SyncPlot)
-        end
-    end
-end
-
-
-@testset "Graphics Function Tests" begin
-    test_plotly_copula_methods()
-end
-
-# Función de prueba para plotly_copula
-function test_multivariate_copula_methods()
-    # Methods to prove
-    Methods = ["scatter", "scatter+hist", "hist2D", "pdf_contours", "cdf_contours", "pdf", "cdf"]
-    
-    for method in Methods
-        for i in [4, 5,6]
-            D_mult = InvGaussianCopula(i, 2.5)
-            samples_mult = rand(D_mult, 300)
-            println("Testing method for multivariate copula: $method")
-            @test_throws ErrorException plotly_copula(D_mult, samples_mult, method)
-        end
-    end 
-    
-    # Trivariate prove
-    for method in Methods
-        for i in [1, 2, 3]
-            T = JoeCopula(3, i)
-            samples_tri = rand(T, 1000)
-            
-            try
-                if length(T) == 3 && method == "scatter3d"
-                    result = plotly_copula(T, samples_tri, method)
-                    @test isa(result, PlotlyJS.SyncPlot)
-                else
-                    println("Testing method for trivariate copula: $method")
-                    @test_throws ErrorException plotly_copula(T, samples_tri, method)
-                end
-            catch ex
-                println("Error in method $method for trivariate copula: $ex")
-            end
-        end
-    end
-end
-
-# Ejecutar la prueba
-@testset "Tests de funciones de gráficos para copulas multivariadas" begin
-    test_multivariate_copula_methods()
-end
-

From 8e1aa29c25197bfa7c7a831955f1470cc5dd5fe3 Mon Sep 17 00:00:00 2001
From: Santymax98 <santymax9807@gmail.com>
Date: Wed, 29 Nov 2023 23:03:53 -0300
Subject: [PATCH 04/13] 	modified:   docs/src/miscellaneous.md 	modified:  
 src/Copulas.jl 	modified:   src/MiscellaneousCopulas/RafteryCopula.jl

---
 docs/src/miscellaneous.md                 | 6 ++++++
 src/Copulas.jl                            | 4 +++-
 src/MiscellaneousCopulas/RafteryCopula.jl | 9 ++++-----
 3 files changed, 13 insertions(+), 6 deletions(-)

diff --git a/docs/src/miscellaneous.md b/docs/src/miscellaneous.md
index 2951a9b0..6198903a 100644
--- a/docs/src/miscellaneous.md
+++ b/docs/src/miscellaneous.md
@@ -29,6 +29,12 @@ PlackettCopula
 FGMCopula
 ```
 
+# Raftery copula
+
+```@docs
+RafteryCopula
+```
+
 ## Survival Copula
 
 ```@docs
diff --git a/src/Copulas.jl b/src/Copulas.jl
index d18418ad..140c31a8 100644
--- a/src/Copulas.jl
+++ b/src/Copulas.jl
@@ -30,12 +30,14 @@ module Copulas
     include("MiscellaneousCopulas/PlackettCopula.jl")
     include("MiscellaneousCopulas/EmpiricalCopula.jl")
     include("MiscellaneousCopulas/FGMCopula.jl")
+    include("MiscellaneousCopulas/RafteryCopula.jl")
     export MCopula,
            WCopula,
            SurvivalCopula,
            PlackettCopula,
            EmpiricalCopula,
-           FGMCopula
+           FGMCopula,
+           RafteryCopula
 
     # Elliptical copulas
     include("EllipticalCopula.jl")
diff --git a/src/MiscellaneousCopulas/RafteryCopula.jl b/src/MiscellaneousCopulas/RafteryCopula.jl
index fc1ceb6f..df19447a 100644
--- a/src/MiscellaneousCopulas/RafteryCopula.jl
+++ b/src/MiscellaneousCopulas/RafteryCopula.jl
@@ -84,13 +84,13 @@ function Distributions._rand!(rng::Distributions.AbstractRNG, R::RafteryCopula{d
     
     dim = length(x)
     
-    # Paso 1: Generar valores independientes u, u_1, ..., u_d desde una distribución uniforme [0, 1]
+    # Step 1: Generate independent values u, u_1, ..., u_d from a uniform distribution [0, 1]
     u = rand(rng, dim+1)
     
-    # Paso 2: Generar j desde una distribución de Bernoulli con parámetro θ
+    # Step 2: Generate j from a Bernoulli distribution with parameter θ
     j = rand(Bernoulli(R.θ),1)
     uj = u[1].^j
-    # Paso 3: Calcular v_1, ..., v_d
+    # Step 3: Calculate v_1, ..., v_d
     for i in 2:dim+1
         x[i] = u[i]^(1 - R.θ) * uj
     end
@@ -102,5 +102,4 @@ function ρ(R::RafteryCopula{d,R}) where {d, P}
     term1 = (d+1)*(2^d-(2-R.θ)^d)-(2^d*R.θ*d)
     term2 = (2-R.θ)^d*(2^d-d-1) 
     return term1/term2
-end
-
+end
\ No newline at end of file

From db385c2b658d486fdd138ce49562cde4516c1951 Mon Sep 17 00:00:00 2001
From: Santymax98 <santymax9807@gmail.com>
Date: Thu, 30 Nov 2023 10:27:07 -0300
Subject: [PATCH 05/13] 	modified:   src/MiscellaneousCopulas/RafteryCopula.jl

---
 src/MiscellaneousCopulas/RafteryCopula.jl | 52 +++++++++++++----------
 1 file changed, 29 insertions(+), 23 deletions(-)

diff --git a/src/MiscellaneousCopulas/RafteryCopula.jl b/src/MiscellaneousCopulas/RafteryCopula.jl
index df19447a..398a1867 100644
--- a/src/MiscellaneousCopulas/RafteryCopula.jl
+++ b/src/MiscellaneousCopulas/RafteryCopula.jl
@@ -19,9 +19,9 @@ where ``u_{(1)}, \\ldots , u_{(d)}`` denote the order statistics of ``u_1, \\ldo
 
 More details about Multivariate Raftery Copula are found in :
 
-    Saali, T., M. Mesfioui, and A. Shabri, 2023: Multivariate Extension of Raftery Copula. Mathematics, 11, 414, https://doi.org/10.3390/math11020414.    
+    [Raftery2023](@cite) Saali, T., M. Mesfioui, and A. Shabri, 2023: Multivariate Extension of Raftery Copula. Mathematics, 11, 414, https://doi.org/10.3390/math11020414. 
     
-    Nelsen, Roger B. An introduction to copulas. Springer, 2006. Exercise 3.6.
+    [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006. Exercise 3.6. 
 
 It has a few special cases:
 - When θ = 0, it is the IndependentCopula.
@@ -41,19 +41,17 @@ struct RafteryCopula{d, P} <: Copula{d}
         end
     end
 end
-function _cdf(R::RafteryCopula, u::Vector{T}) where {T}
-    if length(u) != R.d
-        throw(ArgumentError("Dimension mismatch"))
-    end
-    
+Base.eltype(R::RafteryCopula) = eltype(R.θ)
+
+function _cdf(R::RafteryCopula{d,P}, u::Vector{T}) where {d,P,T}
     # Order the vector u
     u_ordered = sort(u)
     
     term1 = u_ordered[1]
-    term2 = (1 - R.θ) * (1 - R.d) / (1 - R.θ - R.d) * prod(u).^(1/(1 - R.θ))
+    term2 = (1 - R.θ) * (1 - d) / (1 - R.θ - d) * prod(u).^(1/(1 - R.θ))
 
     term3 = 0.0
-    for i in 2:R.d
+    for i in 2:d
         prod_prev = prod(u_ordered[1:i-1])
         term3 += R.θ * (1 - R.θ) / ((1 - R.θ - i) * (2 - R.θ - i)) * prod_prev^(1/(1 - R.θ)) * u_ordered[i]^((2 - R.θ - i) / (1 - R.θ))
     end
@@ -62,17 +60,12 @@ function _cdf(R::RafteryCopula, u::Vector{T}) where {T}
     
     return cdf_value
 end
-
-function Distributions._logpdf(R::RafteryCopula, u::Vector{T}) where {T}
-    if length(u) != R.d
-        throw(ArgumentError("Dimension mismatch"))
-    end
-    
-    # Order the vector u 
+function Distributions._logpdf(R::RafteryCopula{d,P}, u::Vector{T}) where {d,P,T}
+    # Order the vector u
     u_ordered = sort(u)
     
-    term_denominator = (1 - R.θ)^(R.d - 1) * (1 - R.θ - R.d)
-    term_numerator = 1 - R.d - R.θ * u_ordered[R.d]^((1 - R.θ - R.d) / (1 - R.θ))
+    term_denominator = (1 - R.θ)^(d - 1) * (1 - R.θ - d)
+    term_numerator = 1 - d - R.θ * u_ordered[d]^((1 - R.θ - d) / (1 - R.θ))
     term_product = prod(u)^((R.θ) / (1 - R.θ))
     
     logpdf_value = log(term_numerator) - log(term_denominator) + log(term_product)
@@ -88,18 +81,31 @@ function Distributions._rand!(rng::Distributions.AbstractRNG, R::RafteryCopula{d
     u = rand(rng, dim+1)
     
     # Step 2: Generate j from a Bernoulli distribution with parameter θ
-    j = rand(Bernoulli(R.θ),1)
-    uj = u[1].^j
+    j = rand(Distributions.Bernoulli(R.θ), 1)
+    uj = u[1]^j[1]
     # Step 3: Calculate v_1, ..., v_d
     for i in 2:dim+1
-        x[i] = u[i]^(1 - R.θ) * uj
+        x[i-1] = u[i]^(1 - R.θ) * uj
     end
     
     return x
 end
-
 function ρ(R::RafteryCopula{d,R}) where {d, P}
     term1 = (d+1)*(2^d-(2-R.θ)^d)-(2^d*R.θ*d)
     term2 = (2-R.θ)^d*(2^d-d-1) 
     return term1/term2
-end
\ No newline at end of file
+end
+function τ(R::RafteryCopula{d, R}) where {d, P}
+    term1 = (2^(d-1) * factorial(d)) / ((2^(d-1)-1) * prod(i+1-R.θ for i in 2:d))
+    term2 = ((1 - R.θ)^2 * (d^2 - 1)) / ((d-1+R.θ) * (d+1-R.θ) * (2^(d-1)-1))
+    term3_sum = 0.0
+    for k in 2:d
+        term3_sum += (R.θ * (1-R.θ) * (2-R.θ)) / (2^k * factorial(k-1) * (1-R.θ-k) * (2-R.θ-k) * prod(i+1-R.θ for i in k:d))
+    end
+    term3 = (2^d * factorial(d)) / (2^(d-1)-1) * term3_sum
+    
+    term4 = 1 / (2^(d-1)-1)
+    
+    return term1 + term2 - term3 - term4
+end
+

From 59c18cf069c0e17960638a27efe9f77a1305e640 Mon Sep 17 00:00:00 2001
From: Santymax98 <santymax9807@gmail.com>
Date: Thu, 30 Nov 2023 10:39:38 -0300
Subject: [PATCH 06/13] 	modified:   test/margins_uniformity.jl

---
 test/margins_uniformity.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/test/margins_uniformity.jl b/test/margins_uniformity.jl
index 741ab08e..5ae68bf8 100644
--- a/test/margins_uniformity.jl
+++ b/test/margins_uniformity.jl
@@ -25,6 +25,8 @@
         FGMCopula(2,1),
         MCopula(4),
         PlackettCopula(2.0),
+        RafteryCopula(2, 0.2),
+        RafteryCopula(3, 0.5)
         # Others ? Yes probably others too ! 
     )
     n = 1000

From fd9a3db5f7ef09c079a8b20123ce28c5afd3e5c9 Mon Sep 17 00:00:00 2001
From: Santymax98 <132070198+Santymax98@users.noreply.github.com>
Date: Thu, 30 Nov 2023 13:22:41 -0300
Subject: [PATCH 07/13] Update RafteryCopula.jl

---
 src/MiscellaneousCopulas/RafteryCopula.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/MiscellaneousCopulas/RafteryCopula.jl b/src/MiscellaneousCopulas/RafteryCopula.jl
index 398a1867..a160100b 100644
--- a/src/MiscellaneousCopulas/RafteryCopula.jl
+++ b/src/MiscellaneousCopulas/RafteryCopula.jl
@@ -90,12 +90,12 @@ function Distributions._rand!(rng::Distributions.AbstractRNG, R::RafteryCopula{d
     
     return x
 end
-function ρ(R::RafteryCopula{d,R}) where {d, P}
+function ρ(R::RafteryCopula{d,P}) where {d, P}
     term1 = (d+1)*(2^d-(2-R.θ)^d)-(2^d*R.θ*d)
     term2 = (2-R.θ)^d*(2^d-d-1) 
     return term1/term2
 end
-function τ(R::RafteryCopula{d, R}) where {d, P}
+function τ(R::RafteryCopula{d, P}) where {d, P}
     term1 = (2^(d-1) * factorial(d)) / ((2^(d-1)-1) * prod(i+1-R.θ for i in 2:d))
     term2 = ((1 - R.θ)^2 * (d^2 - 1)) / ((d-1+R.θ) * (d+1-R.θ) * (2^(d-1)-1))
     term3_sum = 0.0

From e6d9ddbda87aeccc6f9c0297fca7fb7d9a5908bd Mon Sep 17 00:00:00 2001
From: Santymax98 <132070198+Santymax98@users.noreply.github.com>
Date: Thu, 30 Nov 2023 13:26:02 -0300
Subject: [PATCH 08/13] Update references.bib

---
 docs/src/assets/references.bib | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

diff --git a/docs/src/assets/references.bib b/docs/src/assets/references.bib
index 69a0d3f7..d160a179 100644
--- a/docs/src/assets/references.bib
+++ b/docs/src/assets/references.bib
@@ -718,4 +718,15 @@ @article{derumigny2022
   pages = {104962},
   issn = {0047-259X},
   keywords = {Elliptical generator,Identifiability,Meta-elliptical copulas,Recursive algorithm}
-}
\ No newline at end of file
+}
+
+@article{Raftery2023,
+  title={Multivariate extension of Raftery copula},
+  author={Saali, Tariq and Mesfioui, Mhamed and Shabri, Ani},
+  journal={Mathematics},
+  volume={11},
+  number={2},
+  pages={414},
+  year={2023},
+  publisher={MDPI}
+}

From ec65d3f6093213a2d7cf02629c25a59de152ff9a Mon Sep 17 00:00:00 2001
From: Santymax98 <132070198+Santymax98@users.noreply.github.com>
Date: Thu, 30 Nov 2023 13:33:52 -0300
Subject: [PATCH 09/13] typographical errors

---
 test/RafteryTest.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/test/RafteryTest.jl b/test/RafteryTest.jl
index 63a567f7..b042aaa6 100644
--- a/test/RafteryTest.jl
+++ b/test/RafteryTest.jl
@@ -1,7 +1,7 @@
 @testitem "RafteryCopula Constructor" begin
     for d in [2,3,4]
-        @test isa(RarfteryCopula(d,0.0), IndependentCopula)
-        @test isa(RarfteryCopula(d,1.0), MCopula)
+        @test isa(RafteryCopula(d,0.0), IndependentCopula)
+        @test isa(RafteryCopula(d,1.0), MCopula)
     end    
     @test_throws ArgumentError RafteryCopula(1,0.5)
     @test_throws ArgumentError RafteryCopula(3,-1.5)
@@ -39,4 +39,4 @@ end
     F = RafteryCopula(3,0.5)
     samples = rand(rng,F, n_samples)
     @test size(samples) == (3, n_samples)
-end
\ No newline at end of file
+end

From 0c6c06d8fc9964d4962a26a9f918f09ffcf41090 Mon Sep 17 00:00:00 2001
From: Santymax98 <132070198+Santymax98@users.noreply.github.com>
Date: Thu, 30 Nov 2023 13:48:59 -0300
Subject: [PATCH 10/13] Removing dimension 1 test

---
 test/RafteryTest.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/test/RafteryTest.jl b/test/RafteryTest.jl
index b042aaa6..8519095b 100644
--- a/test/RafteryTest.jl
+++ b/test/RafteryTest.jl
@@ -3,7 +3,6 @@
         @test isa(RafteryCopula(d,0.0), IndependentCopula)
         @test isa(RafteryCopula(d,1.0), MCopula)
     end    
-    @test_throws ArgumentError RafteryCopula(1,0.5)
     @test_throws ArgumentError RafteryCopula(3,-1.5)
     @test_throws ArgumentError RafteryCopula(2, 2.6)
 end

From c86bfb16bd75dd9ea0731b1c990a613bf6696393 Mon Sep 17 00:00:00 2001
From: Oskar Laverny <oskar.laverny@gmail.com>
Date: Thu, 30 Nov 2023 17:54:43 +0100
Subject: [PATCH 11/13] Modify docstring slightly

---
 src/MiscellaneousCopulas/RafteryCopula.jl | 15 ++++++---------
 1 file changed, 6 insertions(+), 9 deletions(-)

diff --git a/src/MiscellaneousCopulas/RafteryCopula.jl b/src/MiscellaneousCopulas/RafteryCopula.jl
index a160100b..3863421c 100644
--- a/src/MiscellaneousCopulas/RafteryCopula.jl
+++ b/src/MiscellaneousCopulas/RafteryCopula.jl
@@ -2,7 +2,7 @@
     RafteryCopula{d, P}
 
 Fields:
-  - θ::Real - parameter
+    - θ::Real - parameter
 
 Constructor
 
@@ -14,18 +14,15 @@ The Multivariate Raftery Copula of dimension d is arameterized by ``\\theta \\in
 C_{\\theta}(\\mathbf{u}) = u_{(1)} + \\frac{(1 - \\theta)(1 - d)}{1 - \\theta - d} \\left(\\prod_{j=1}^{d} u_j\\right)^{\\frac{1}{1-\\theta}} - \\sum_{i=2}^{d} \\frac{\\theta(1-\\theta)}{(1-\\theta-i)(2-\\theta-i)} \\left(\\prod_{j=1}^{i-1}u_{(j)}\\right)^{\\frac{1}{1-\\theta}}u_{(i)}^{\\frac{2-\\theta-i}{1-\\theta}}
 ```
 
-
-where ``u_{(1)}, \\ldots , u_{(d)}`` denote the order statistics of ``u_1, \\ldots ,u_d``.
-
-More details about Multivariate Raftery Copula are found in :
-
-    [Raftery2023](@cite) Saali, T., M. Mesfioui, and A. Shabri, 2023: Multivariate Extension of Raftery Copula. Mathematics, 11, 414, https://doi.org/10.3390/math11020414. 
-    
-    [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006. Exercise 3.6. 
+where ``u_{(1)}, \\ldots , u_{(d)}`` denote the order statistics of ``u_1, \\ldots ,u_d``. More details about Multivariate Raftery Copula are found in the references below.
 
 It has a few special cases:
 - When θ = 0, it is the IndependentCopula.
 - When θ = 1, it is the the Fréchet upper bound
+
+References: 
+* [Raftery2023](@cite) Saali, T., M. Mesfioui, and A. Shabri, 2023: Multivariate Extension of Raftery Copula. Mathematics, 11, 414, https://doi.org/10.3390/math11020414. 
+* [nelsen2006](@cite) Nelsen, Roger B. An introduction to copulas. Springer, 2006. Exercise 3.6. 
 """
 struct RafteryCopula{d, P} <: Copula{d}
     θ::P  # Copula parameter

From 0ce8dcdb612c9a9909818bc841c0cd669fac3763 Mon Sep 17 00:00:00 2001
From: Oskar Laverny <oskar.laverny@gmail.com>
Date: Thu, 30 Nov 2023 18:05:21 +0100
Subject: [PATCH 12/13] errors in the docs

---
 docs/src/miscellaneous.md | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/docs/src/miscellaneous.md b/docs/src/miscellaneous.md
index 5081209f..27af7f2f 100644
--- a/docs/src/miscellaneous.md
+++ b/docs/src/miscellaneous.md
@@ -16,14 +16,12 @@ PlackettCopula
 
 Farlie-Gumbel-Morgenstern (FGM) copula
 
-# Raftery copula
-
 ```@docs
-RafteryCopula
+FGMCopula
 ```
 
-## Survival Copula
+# Raftery copula
 
 ```@docs
-SurvivalCopula
+RafteryCopula
 ```

From 1920d01255b1f5562915631b520f9c023944b273 Mon Sep 17 00:00:00 2001
From: Santymax98 <132070198+Santymax98@users.noreply.github.com>
Date: Thu, 30 Nov 2023 15:12:20 -0300
Subject: [PATCH 13/13] add tests of CDF and PDF RafteryTest.jl

---
 test/RafteryTest.jl | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)

diff --git a/test/RafteryTest.jl b/test/RafteryTest.jl
index 8519095b..b7d98b55 100644
--- a/test/RafteryTest.jl
+++ b/test/RafteryTest.jl
@@ -17,6 +17,17 @@ end
         cdf_value = cdf(F, u)
         @test cdf_value >= 0 && cdf_value <= 1
     end
+    examples = [
+        ([0.2, 0.5], [1.199432, 1e-5], 0.8),
+        ([0.3, 0.8], [0.2817, 1e-5], 0.5),
+        ([0.1, 0.2, 0.3], [0.08325884, 1e-5], 0.5),
+        ([0.4, 0.8, 0.2], [0.120415, 1e-5], 0.1),
+    ]
+        
+    for (u, expected, θ) in examples
+        copula = RafteryCopula(length(u), θ)
+        @test cdf(copula, u) ≈ expected[1] atol=expected[2]
+    end    
 end
 
 @testset "RafteryCopula PDF" begin
@@ -29,8 +40,20 @@ end
         pdf_value = pdf(F, u)
         @test pdf_value >= 0
     end
+    examples = [
+        ([0.2, 0.5], [0.114055555, 1e-4], 0.8),
+        ([0.3, 0.8], [0.6325, 1e-4], 0.5),
+        ([0.1, 0.2, 0.3], [1.9945086, 1e-4], 0.5),
+        ([0.4, 0.8, 0.2], [0.939229, 1e-4], 0.1),
+    ]
+        
+    for (u, expected, θ) in examples
+        copula = RafteryCopula(length(u), θ)
+        @test pdf(copula, u) ≈ expected[1] atol=expected[2]
+    end
 end
 
+
 @testitem "RafteryCopula Sampling" begin
     using StableRNGs
     rng = StableRNG(123)