DWreg (version 1.0)

dw.meanvar: 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.

Value

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

Details

The mean and variance are computed using the following approximations: $$E(X)=\sum_{k=1}^{M} q^{k^{\beta}}$$ $$E(X^2)=\sum_{k=1}^{M} (2k-1)q^{k^{\beta}} = 2\sum_{k=1}^{M} kq^{k^{\beta}}-E(X)$$

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)