# Edweibull: Expected values In DiscreteWeibull: Discrete Weibull Distributions (Type 1 and 3)

## Description

First and second order moments, variance and expected value of the reciprocal for the type 1 discrete Weibull distribution

## Usage

 ```1 2 3 4``` ```Edweibull(q, beta, eps = 1e-04, nmax = 1000, zero = FALSE) E2dweibull(q, beta, eps = 1e-04, nmax = 1000, zero = FALSE) Vdweibull(q, beta, eps = 1e-04, nmax = 1000, zero = FALSE) ERdweibull(q, beta, eps = 1e-04, nmax = 1000) ```

## Arguments

 `q` first parameter `beta` second parameter `eps` error threshold for the numerical computation of the expected value `nmax` maximum value considered for the numerical approximate computation of the expected value; `zero` `TRUE`, if the support contains 0; `FALSE` otherwise

## Details

The expected value is numerically computed considering a truncated support: integer values smaller than or equal to 2F^{-1}(1-eps;q,β) are considered, where F^{-1} is the inverse of the cumulative distribution function (implemented by the function `qdweibull`). However, if such value is greater than `nmax`, the expected value is computed recalling the formula of the expected value of the corresponding continuous Weibull distribution (see the reference), adding 0.5. Similar arguments apply to the other moments.

## Value

the (approximate) expected values of the discrete Weibull distribution: `Edweibull` gives the first order moment, `E2dweibull` the second order moment, `Vdweibull` the variance, `ERdweibull` the expected value of the reciprocal (only if `zero` is `FALSE`)

## Author(s)

Alessandro Barbiero

## References

M. S. A. Khan, A. Khalique, and A. M. Abouammoh (1989) On estimating parameters in a discrete Weibull distribution, IEEE Transactions on Reliability, 38(3), pp. 348-350

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```q <- 0.75 beta <- 1.25 Edweibull(q, beta) E2dweibull(q, beta) Vdweibull(q, beta) ERdweibull(q, beta) # if beta=0.75... beta <- 0.75 Edweibull(q, beta) Edweibull(q, beta, nmax=100) # here above, the approximation through the continuous model intervenes # if beta=1... beta <- 1 Edweibull(q, beta) # which equals... 1/(1-q) ```

### Example output

```Loading required package: Rsolnp
[1] 3.037885
[1] 13.3628
[1] 4.134054
[1] 0.4976714
[1] 6.806787
[1] 6.769456
[1] 4
[1] 4
```

DiscreteWeibull documentation built on May 29, 2017, 11:19 p.m.