Runuran (version 0.40)

udlogarithmic: UNU.RAN object for Logarithmic distribution

Description

Create UNU.RAN object for a Logarithmic distribution with shape parameter shape.

[Distribution] -- Logarithmic.

Usage

udlogarithmic(shape, lb = 1, ub = Inf)

Value

An object of class "unuran.discr".

Arguments

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 domain of the distribution can be truncated to the interval (lb,ub).

References

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

unuran.discr.

Examples

## Create distribution object for Logarithmic distribution
dist <- udlogarithmic(shape=0.3)
## Generate generator object; use method DARI
gen <- darid.new(dist)
## Draw a sample of size 100
x <- ur(gen,100)