UnivRNG (version 1.2.3)

draw.left.truncated.gamma: Generates variates from left truncated Gamma distribution

Description

This function implements pseudo-random number generation for a left-truncated gamma distribution with pdf

$$f(x|\alpha, \beta) = \frac{1}{(\Gamma(\alpha)-\Gamma_{\tau/\beta}(\alpha))\beta^{\alpha}}x^{\alpha-1}e^{-x/\beta}$$

for \(0<\tau\leq x\), and min(\(\tau\), \(\beta\))>0 where \(\alpha\) and \(\beta\) are the shape and scale parameters, respectively, \(\tau\) is the cutoff point at which truncation occurs, and \(\Gamma_{\tau/\beta}\) is the incomplete gamma function.

Usage

draw.left.truncated.gamma(nrep,alpha,beta,tau)

Arguments

nrep

Number of data points to generate.

alpha

Shape parameter for the desired gamma distribution.

beta

Scale parameter fot the desired gamma distribution.

tau

Point of left truncation.

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

Dagpunar, J. S. (1978). Sampling of variates from a truncated gamma distribution. Journal of Statistical Computation and Simulation, 8, 59-64.

Examples

# NOT RUN {
draw.left.truncated.gamma(nrep=100000,alpha=5,beta=1,tau=0.5)

draw.left.truncated.gamma(nrep=100000,alpha=2,beta=2,tau=0.1)
# }