Runuran (version 0.40)

urlogarithmic: UNU.RAN Logarithmic random variate generator

Description

UNU.RAN random variate generator for the Logarithmic distribution with shape parameter shape. It also allows sampling from the truncated distribution.

[Special Generator] -- Sampling Function: Logarithmic.

Usage

urlogarithmic(n, shape, lb = 1, ub = Inf)

Arguments

n

size of required sample.

shape

shape parameter. Must be between 0 and 1.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

Details

The Logarithmic distribution with parameters shape \(= \theta\) has density $$ f(x) = -\log(1-\theta) \theta^x / x $$ for \(x = 1, 2, \ldots\) and \(0 < \theta < 1\).

The generation algorithm uses guide table based inversion when the tails are not too heavy and method ‘DARI’ otherwise. The parameters lb and ub can be used to generate variates from the Logarithmic distribution truncated to the interval (lb,ub).

References

W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg.

N.L. Johnson, S. Kotz, and A.W. Kemp (1992): Univariate Discrete Distributions, 2nd edition. John Wiley & Sons, Inc., New York. Chap.7, p.285.

See Also

runif and .Random.seed about random number generation and unuran for the UNU.RAN class.

Examples

## Create a sample of size 1000
x <- urlogarithmic(n=1000,shape=0.3)