| draw.gamma.alpha.less.than.one {UnivRNG} | R Documentation |
Generates variation from Gamma distribution with \alpha<1
Description
This function implements pseudo-random number generation for a gamma distribution for \alpha<1 with pdf
f(x|\alpha,\beta)=\frac{1}{\Gamma(\alpha)\beta^{\alpha}}x^{\alpha-1}e^{-x/\beta}
for 0 \leq x < \infty and \min(\alpha,\beta)>0 where \alpha and \beta are the shape and scale parameters, respectively.
Usage
draw.gamma.alpha.less.than.one(nrep,alpha,beta)
Arguments
nrep |
Number of data points to generate. |
alpha |
Shape parameter for desired gamma distribution. Must be less than 1. |
beta |
Scale parameter for desired gamma distribution. |
Value
A list of length five containing generated data, the theoretical mean, the empirical mean, the theoretical variance, and the empirical variance with names y, theo.mean, emp.mean, theo.var, and emp.var, respectively.
References
Ahrens, J. H., & Dieter, U. (1974). Computer methods for sampling from gamma, beta, poisson and binomial distributions. Computing, 1, 223-246.
Examples
draw.gamma.alpha.less.than.one(nrep=100000,alpha=0.5,beta=2)