Expanded semicircle distribution

Author: jiahao

src/DistributionTemplate.jl

@@ -1,66 +0,0 @@
-using Distributions
-
-immutable Semicircle <: ContinuousUnivariateDistribution
-    mean::Float64
-    radius::Float64
-    Semicircle(mu, r) = r > 0 ? new(float64(mu), float64(r)) : error("radius r must be positive")
-end
-
-#Standard (normalized) - note this is NOT the standard used in to RMT (r = 2)
-Semicircle(mu) = Semicircle(mu, 1.0)
-Semicircle() = Semicircle(0.0, 1.0)
-
-# Properties
-# For convenience, this is ordered like the Wikipedia infobox template ;)
-
-#Probability density function
-function pdf(d::Semicircle, x::Real)
-    r, a = d.mean, d.radius
-    return 2/(pi*r^2) * sqrt(r^2 - (x-a)^2)
-end
-
-#Cumulative density function
-function cdf(d::Semicircle, x::Real)
-    r, a = d.mean, d.radius
-    if x < -a
-        return 0.0
-    elseif x > a
-        return 1.0
-    else
-        return 0.5 + (x-a)/(pi*r^2) * sqrt(r^2 - (x-a)^2) + 1/pi * asin((x-a)/r)
-    end
-end
-
-function logpdf(d::Laplace, x::Real)
-    log(pdf(d, x))
-end
-function quantile(d::Laplace, p::Real)
-    0.0
-end
-
-mean(d::Semicircle) = d.mean
-median(d::Semicircle) = d.mean
-mode(d::Semicircle) = d.mean
-
-std(d::Semicircle) = (d.radius/2)
-var(d::Semicircle) = (d.radius/2)^2
-skewness(d::Semicircle) = 0.0
-kurtosis(d::Semicircle) = 2.0
-entropy(d::Semicircle) = log(pi*R) - 0.5
-
-## Moment generating function
-function mgf(d::Semicircle, t::Real)
-    r = t * d.mean
-    2 * besseli(1, r)/r
-end
-
-# Characteristic function
-function cf(d::Semicircle, t::Real)
-    r = t * d.mean
-    2 * besselj(1, r)/r
-end
-
-## Common methods
-#XXX Use the fact that Semicircle(0.5, 0.5) = Beta(1.5, 1.5)
-rand(d::Semicircle) = 2*(rand(Beta(1.5, 1.5) - 0.5))
-insupport(d::Normal, x::Number) = real_valued(x) & (abs(x) <= d.radius)

src/GaussianDensities.jl

@@ -5,10 +5,11 @@ module RandomMatrices
 
     #Classical Gaussian matrix ensembles
     include("GaussianEnsembleSamples.jl")
-    #Classical univariate distributions
-    include("GaussianDensities.jl")
+    # Classical univariate distributions
+    ####################################
+    include("densities/Semicircle.jl")
     #Tracy-Widom distribution
-    include("TracyWidom.jl")
+    include("densities/TracyWidom.jl")
 
     #Fast histogrammer for matrix eigenvalues
     include("FastHistogram.jl")

src/RandomMatrices.jl

@@ -0,0 +1,158 @@
+#A template for defining a new distribution
+importall Distributions
+# Note: these don't exist in Distributions.jl yet
+export ThisDistribution, moment, cumulant, freecumulant, cf, cgf, mgf
+
+#Change type below to an actual type:
+# DiscreteUnivariateDistribution    
+# ContinuousUnivariateDistribution  
+# DiscreteMultivariateDistribution  
+# ContinuousMultivariateDistribution
+# ContinuousMatrixDistribution      
+# DiscreteMatrixDistribution        
+type ThisDistribution <: Distribution
+    data::Any #Internal fields
+    #beta::Real 
+    ThisDistribution(data) = new(data) #Constructor
+end
+
+#Standardized distribution - mean 0, variance 1
+
+#Methods for the distribution
+#The methods commented out below have default fallback methods
+
+# Distribution function methods
+###############################
+
+# complementary cdf i.e. 1 - cdf
+#ccdf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# cumulative distribution function
+cdf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+#complementary quantile based on log probability
+#invlogccdf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# quantile based on log probability
+#invlogcdf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))     
+
+# ccdf returning log-probability
+#logccdf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# cdf returning log-probability
+#logcdf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# log probability density
+#logpdf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# probability density function
+pdf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# inverse of cdf (defined for p in (01))
+quantile(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# complementary quantile (i.e. using prob in right hand tail)
+#cquantile(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# predicate is x in the support of the distribution?
+insupport(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))     
+
+
+#Entropy methods
+################
+
+# entropy of distribution in bits
+#binaryentropy(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# entropy of distribution in nats
+entropy(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))       
+
+#Measures of central tendency methods
+#####################################
+
+# mean of distribution
+mean(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# median of distribution
+median(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# mode(s) of distribution as vector
+modes(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# standard deviation of distribution
+#std(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# variance of distribution
+var(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# skewness of the distribution
+skewness(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# kurtosis of the distribution
+kurtosis(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# excess kurtosis of the distribution
+excess_kurtosis(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# moment of distribution
+moment(X::ThisDistribution, order::Integer)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# cumulant of distribution
+cumulant(X::ThisDistribution, order::Integer)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# free cumulant of distribution
+freecumulant(X::ThisDistribution, order::Integer)=error(string("Not defined for ", typeof(X), " distribution"))
+
+
+#Generating function methods
+############################
+
+# characteristic function 
+cf(X::ThisDistribution, t::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# cumulant generating function
+cgf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# moment generating function
+mgf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))
+
+#Sampling methods
+#################
+
+# random sampler
+rand(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+
+#Regression methods for generalized linear models (GLM)
+#######################################################
+
+# canonical link function for a distribution
+canonicallink(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# deviance of fitted and observed responses
+#deviance(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# vector of squared deviance residuals
+#devresid(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# fit a distribution to data
+fit(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# link function mapping mu to eta the linear predictor
+linkfun(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# inverse link mapping eta to mu
+linkinv(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# derivative of inverse link function
+mueta(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# starting values of mean vector in GLMs
+#mustart(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# validity check on linear predictor
+valideta(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+
+# validity check on mean vector
+validmu(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))
+