enforce consistent naming for Epanechnikov & Exponential

src/univariate/continuous/epanechnikov.jl

@@ -1,51 +1,63 @@
 immutable Epanechnikov <: ContinuousUnivariateDistribution
-    location::Float64
-    scale::Float64
-    function Epanechnikov(l::Real, s::Real)
-        s > zero(s) || error("scale must be positive")
-        @compat new(Float64(l), Float64(s))
+    μ::Float64
+    σ::Float64
+    function Epanechnikov(μ::Real, σ::Real)
+        σ > zero(σ) ||
+            throw(ArgumentError("Epanechnikov: σ must be positive."))
+        @compat new(Float64(μ), Float64(σ))
     end
-end
 
-Epanechnikov(location::Real) = Epanechnikov(location, 1.0)
-Epanechnikov() = Epanechnikov(0.0, 1.0)
+    Epanechnikov(μ::Real) = @compat new(Float64(μ), 1.0)
+    Epanechnikov() = new(0.0, 1.0)
+end
 
-@distr_support Epanechnikov d.location-d.scale d.location+d.scale
+@distr_support Epanechnikov d.μ - d.σ d.μ + d.σ
 
 ## Parameters
-params(d::Epanechnikov) = (d.location, d.scale)
+
+location(d::Epanechnikov) = d.μ
+scale(d::Epanechnikov) = d.σ
+params(d::Epanechnikov) = (d.μ, d.σ)
 
 ## Properties
-mean(d::Epanechnikov) = d.location
-median(d::Epanechnikov) = d.location
-mode(d::Epanechnikov) = d.location
+mean(d::Epanechnikov) = d.μ
+median(d::Epanechnikov) = d.μ
+mode(d::Epanechnikov) = d.μ
 
-var(d::Epanechnikov) = d.scale*d.scale/5
+var(d::Epanechnikov) = d.σ^2 / 5
 skewness(d::Epanechnikov) = 0.0
-kurtosis(d::Epanechnikov) = 3/35-3
+kurtosis(d::Epanechnikov) = -2.914285714285714  # 3/35-3
 
 ## Functions
-function pdf(d::Epanechnikov, x::Real)   
-    u = abs(x - d.location)/d.scale
-    u >= 1 ? 0.0 : 0.75*(1-u*u)/d.scale
+function pdf(d::Epanechnikov, x::Float64)
+    u = abs(x - d.μ) / d.σ
+    u >= 1 ? 0.0 : 0.75 * (1 - u^2) / d.σ
 end
-function cdf(d::Epanechnikov, x::Real)
-    u = (x - d.location)/d.scale
-    u <= -1 ? 0.0 : u >= 1 ? 1.0 : 0.5+u*(0.75-0.25*u*u)
+
+function cdf(d::Epanechnikov, x::Float64)
+    u = (x - d.μ) / d.σ
+    u <= -1 ? 0.0 :
+    u >= 1 ? 1.0 :
+    0.5 + u * (0.75 - 0.25 * u^2)
 end
-function ccdf(d::Epanechnikov, x::Real)
-    u = (d.location - x)/d.scale
-    u <= -1 ? 1.0 : u >= 1 ? 0.0 : 0.5+u*(0.75-0.25*u*u)
+
+function ccdf(d::Epanechnikov, x::Float64)
+    u = (d.μ - x) / d.σ
+    u <= -1 ? 1.0 :
+    u >= 1 ? 0.0 :
+    0.5 + u * (0.75 - 0.25 * u^2)
 end
 
 @quantile_newton Epanechnikov
 
-function mgf(d::Epanechnikov, t::Real)
-    a = d.scale*t
-    a == 0 ? one(a) : 3.0*exp(d.location*t)*(cosh(a)-sinh(a)/a)/(a*a)
+function mgf(d::Epanechnikov, t::Float64)
+    a = d.σ * t
+    a == 0 ? 1.0 :
+    3.0 * exp(d.μ * t) * (cosh(a) - sinh(a) / a) / a^2
 end
 
-function cf(d::Epanechnikov, t::Real)
-    a = d.scale*t
-    a == 0 ? complex(one(a)) : -3.0*exp(im*d.location*t)*(cos(a)-sin(a)/a)/(a*a)
+function cf(d::Epanechnikov, t::Float64)
+    a = d.σ * t
+    a == 0 ? 1.0+0.0im :
+    -3.0 * exp(im * d.μ * t) * (cos(a) - sin(a) / a) / a^2
 end

src/univariate/continuous/exponential.jl

@@ -1,11 +1,11 @@
 immutable Exponential <: ContinuousUnivariateDistribution
-    β::Float64 		# note: scale not rate
+    θ::Float64 		# note: scale not rate
 
-    function Exponential(β::Real)
-        β > zero(β) || error("scale must be positive")
-        @compat new(Float64(β))
+    function Exponential(θ::Real)
+        θ > zero(θ) ||
+            throw(ArgumentError("Exponential: scale must be positive"))
+        @compat new(Float64(θ))
     end
-
     Exponential() = new(1.0)
 end
 
@@ -14,33 +14,33 @@ end
 
 #### Parameters
 
-scale(d::Exponential) = d.β
-rate(d::Exponential) = 1.0 / d.β
+scale(d::Exponential) = d.θ
+rate(d::Exponential) = 1.0 / d.θ
 
-params(d::Exponential) = (d.β,)
+params(d::Exponential) = (d.θ,)
 
 
 #### Statistics
 
-mean(d::Exponential) = scale(d)
+mean(d::Exponential) = d.θ
 
-median(d::Exponential) = logtwo * scale(d)
+median(d::Exponential) = logtwo * d.θ
 
 mode(d::Exponential) = 0.0
 
-var(d::Exponential) = scale(d)^2
+var(d::Exponential) = d.θ^2
 
 skewness(d::Exponential) = 2.0
 
 kurtosis(d::Exponential) = 6.0
 
-entropy(d::Exponential) = 1.0 + log(scale(d))
+entropy(d::Exponential) = 1.0 + log(d.θ)
 
 
 #### Evaluation
 
-zval(d::Exponential, x::Float64) = x / d.β
-xval(d::Exponential, z::Float64) = z * d.β
+zval(d::Exponential, x::Float64) = x / d.θ
+xval(d::Exponential, z::Float64) = z * d.θ
 
 pdf(d::Exponential, x::Float64) = (λ = rate(d); x < 0.0 ? 0.0 : λ * exp(-λ * x))
 logpdf(d::Exponential, x::Float64) =  (λ = rate(d); x < 0.0 ? -Inf : log(λ) - λ * x)