Adds template for defining distributions

Author: jiahao

src/DistributionTemplate.jl

@@ -0,0 +1,72 @@
+#A template for defining a new distribution
+importall Distributions
+# Note: these don't exist in Distributions.jl yet
+export 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
+
+#Methods for the distribution
+#The methods commented out below have default fallback methods
+
+#Distribution function methods
+#ccdf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))          # complementary cdf i.e. 1 - cdf
+cdf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))           # cumulative distribution function
+#cquantile(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))     # complementary quantile (i.e. using prob in right hand tail)
+#invlogccdf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))    # complementary quantile based on log probability
+#invlogcdf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))     # quantile based on log probability
+#logccdf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))       # ccdf returning log-probability
+#logcdf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))        # cdf returning log-probability
+#logpdf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))        # log probability density
+#logpmf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))        # log probability mass
+#pmf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))           # probability mass function (DiscreteDistribution)
+pdf(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))           # probability density function (ContinuousDistribution)
+quantile(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))      # inverse of cdf (defined for p in (01))
+insupport(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))     # predicate is x in the support of the distribution?
+
+#Entropy methods
+#binaryentropy(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution")) # entropy of distribution in bits
+entropy(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))       # entropy of distribution in nats
+
+#Measures of central tendency methods
+mean(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))          # mean of distribution
+median(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))        # median of distribution
+modes(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))         # mode(s) of distribution as vector
+kurtosis(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))      # kurtosis of the distribution
+skewness(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))      # skewness of the distribution
+#std(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))           # standard deviation of distribution
+var(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))           # variance of distribution
+moment(X::ThisDistribution, order::Integer)=error(string("Not defined for ", typeof(X), " distribution"))        # moment of distribution
+cumulant(X::ThisDistribution, order::Integer)=error(string("Not defined for ", typeof(X), " distribution"))      # cumulant of distribution
+freecumulant(X::ThisDistribution, order::Integer)=error(string("Not defined for ", typeof(X), " distribution"))  # free cumulant of distribution
+
+#Generating function methods
+cf(X::ThisDistribution, t::Real)=error(string("Not defined for ", typeof(X), " distribution"))   # characteristic function 
+cgf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))  # cumulant generating function
+mgf(X::ThisDistribution, x::Real)=error(string("Not defined for ", typeof(X), " distribution"))  # moment generating function
+
+#Sampling methods
+rand(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))          # random sampler
+
+#Regression methods for generalized linear models (GLM)
+canonicallink(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution")) # canonical link function for a distribution
+#deviance(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))      # deviance of fitted and observed responses
+#devresid(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))      # vector of squared deviance residuals
+fit(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))           # fit a distribution to data
+linkfun(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))       # link function mapping mu to eta the linear predictor
+linkinv(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))       # inverse link mapping eta to mu
+mueta(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))         # derivative of inverse link function
+#mustart(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))       # starting values of mean vector in GLMs
+valideta(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))      # validity check on linear predictor
+validmu(X::ThisDistribution)=error(string("Not defined for ", typeof(X), " distribution"))       # validity check on mean vector
+