dw.meanvar: Mean and Variance of Discrete Weibull

In DWreg: Parametric Regression for Discrete Response

Mean and Variance of Discrete Weibull

Description

Mean and variance of a discrete Weibull distribution with parameters q and beta.

Usage

dw.meanvar(q,beta,M)

Arguments

q, beta	Parameters of the distribution
M	Maximum value of the summation. Default value is 1000.

Details

The mean and variance are computed using the following approximations:

E(X)=\sum_{k=1}^{M} q^{k^{\beta}}

E(X^2)=\sum_{k=1}^{M} (2k-1)q^{k^{\beta}} = 2\sum_{k=1}^{M} kq^{k^{\beta}}-E(X)

Value

The function returns the mean and variance of a DW distribution with parameters q and beta.

Author(s)

Veronica Vinciotti

References

Khan M, Khalique A, Abouammoth A. On estimating parameters in a discrete Weibull distribution. IEEE transactions on Reliability 1989; 38(3):348-350.

Examples

dw.meanvar(q=0.9,beta=1.5)
#compare with sample mean/variance from a random sample
x<-rdw(1000,q=0.9,beta=1.5)
mean(x)
var(x)

DWreg documentation built on June 8, 2025, 10:20 a.m.