# Ediweibull: First and second order moments In DiscreteInverseWeibull: Discrete Inverse Weibull Distribution

## Description

First and second order moments of the discrete inverse Weibull distribution

## Usage

 `1` ```Ediweibull(q, beta, eps = 1e-04, nmax = 1000) ```

## Arguments

 `q` the value of the q parameter `beta` the value of the β parameter `eps` error threshold for the approximated computation of the moments `nmax` a first maximum value of the support considered for the approximated computation of the moments

## Details

For a discrete inverse Weibull distribution we have E(X;q,β)=∑_{x=0}^{+∞} 1-F(x;q, β) and E(X^2;q,β)=2∑_{x=1}^{+∞} x(1-F(x;q, β))+E(X;q, β). The expected values are numerically computed considering a truncated support: integer values smaller than or equal to \min(nmax;F^{-1}(1-eps;q,β)), where F^{-1} is the inverse of the cumulative distribution function (implemented by the function `qdiweibull`). Increasing the value of `nmax` or decreasing the value of `eps` improves the approximation, but slows down the calculation speed

## Value

a list comprising the (approximate) first and second order moments of the discrete inverse Weibull distribution. Note that the first moment is finite iff β is greater than 1; the second order moment is finite iff β is greater than 2

## References

Khan M.S., Pasha G.R., Pasha A.H. (2008) Theoretical Analysis of Inverse Weibull Distribution, WSEAS Trabsactions on Mathematics 2(7): 30-38

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# Ex.1 q<-0.75 beta<-1.25 Ediweibull(q, beta) # Ex.2 q<-0.5 beta<-2.5 Ediweibull(q, beta) # Ex.3 q<-0.4 beta<-4 Ediweibull(q, beta) ```

DiscreteInverseWeibull documentation built on May 29, 2017, 5:46 p.m.