Distribution and Probability Functions

These are density and distribution functions for various univariate and multvariate densities. Random number functions are in a separate section.

%betainc(x,a,b)	Incomplete beta function
%bicdf(x0,y0,rho)	Bivariate standard Normal CDF with correlation Rho
%binomial(x,n)	Binomial coefficient
%binomialcdf(k,n,p)	Cumulative binomial probability
%binomialk(k,n,p)	Binomial probability
%cdf(x)	Cumulative density function of standard Normal
%chisqr(x,r)	Chi-squared tail probability
%chisqrdensity(x,r)	Density of the Chi-squared
%chisqrnc(x,r,nc)	Non-central chi-square CDF
%chisqrncdensity(x,r,nc)	Density of the non-central chi-squared
%density(x)	Standard Normal density function
%digamma(x)	Digamma function (derivative of the log gamma)
%dmills(x)	Derivative of the inverse Mills’ ratio
%factorial(x)	Factorial function
%ftest(x,n,m)	F test tail probability
%gamma(a)	Gamma function
%gammainc(x,a)	Incomplete gamma function
%gedcdf(x,s)	CDF of GED distribution
%gevcdf(x,k,m,s)	CDF of generalized extreme value distribution
%gpcdf(x,k,m,s)	CDF of generalized Pareto distribution
%invchisqr(p,r)	Inverse Chi-squared test
%invchisqrnc(p,r)	Inverse non-central chi-square CDF
%invftest(p,n,m)	Inverse F-test
%invged(p,c)	Inverse GED CDF
%invgev(p,k,m,s)	Inverse Generalized Extreme Value CDF
%invgp(p,k,m,s)	Inverse generalized Pareto CDF
%invnormal(p)	Inverse Normal distribution CDF
%invtcdf(p,d)	Inverse Student-t CDF
%invttest(p,r)	Inverse Student-t test
%invztest(p)	Inverse two-tailed Normal
%lnbeta(a,b)	Natural log of Beta function
%lngamma(x)	Natural log of the Gamma function
%lnlogistic(x)	Log of the logistic CDF
%logbetadensity(x,a,b)	Log density of Beta distribution
%logcdf(v,x)	Log of the Normal CDF
%logconcdensity(S,v)	Log concentrated multivariate Normal density
%logdensity(A,v)	Log multivariate or univariate Normal density
%logdensitycv(S1,S2,n)	Log multivariate Normal density as function of S
%logdensitydiag(v,u)	Diagonal multivariate log Normal density
%logdirichlet(x,d)	Log Dirichlet density (x and d are VECTOR's)
%loggammadensity(X,A,B)	Log density of gamma, with shape parameter a and scale b.
%loggeddensity(x,c,v)	Log GED density
%loggevdensity(x,k,mu,s)	Log GEV density
%loggpdensity(x,k,mu,s)	Log generalized Pareto density
%loginvchisqrdensity(x,df,scale)	Log inverse (scaled) chi-squared density
%loginvgammadensity(x,a,b)	Log inverse gamma density
%logistic(x)	Logistic function
%lognegbin(x,r,p)	Log of the negative binomial density
%logpoissonk(mean,k)	Log of Poisson probability for k successes
%logtdensity(V,U,nu)	Log univariate or multivariate t density
%logtdensitystd(V,U,nu)	Standardized log univariate or multivariate t density. This is equivalent to:%logtdensity(v*nu/(nu-2),u,nu)
%mills(x)	Inverse Mills’ ratio
%negbin(x,r,p)	Negative binomial density
%nyblomtest(x,p)	Nyblom fluctuations test significance level
%poisson(mean,k)	Poisson cumulative distribution
%poissonk(mean,k)	Poisson probability of having exactly k successes
%qformpdf(A,x)	CDF of quadratic form of Normals
%qformdpdf(D,x)	CDF of diagonal quadratic form
%tcdf(x,nu)	CDF for a Student-t distribution
%tcdfnc(x,r)	CDF for non-central t density
%tdensity(x,r)	Student-t density
%tdensitync(x,r)	Non-central t density
%trigamma(x)	Trigamma function (second derivative of log gamma)
%ttest(x,n)	Two-tailed t test
%ztest(x)	Two-tailed standard Normal probability