First and second order moments of the discrete inverse Weibull distribution

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

`q` |
the value of the |

`beta` |
the value of the |

`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 |

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

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

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

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)
``` |

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