# ddiweibull: The discrete inverse Weibull distribution In DiscreteInverseWeibull: Discrete Inverse Weibull Distribution

## Description

Probability mass function, distribution function, quantile function and random generation for the discrete inverse Weibull distribution with parameters q and β

## Usage

 ```1 2 3 4``` ```ddiweibull(x, q, beta) pdiweibull(x, q, beta) qdiweibull(p, q, beta) rdiweibull(n, q, beta) ```

## Arguments

 `x` a vector of quantiles `p` a vector of probabilities `q` the value of the first parameter, q `beta` the value of the second parameter, β `n` the sample size

## Details

The discrete inverse Weibull distribution has probability mass function given by P(X=x;q,β)=q^{(x)^{-β}}-q^{(x-1)^{β}}, x=1,2,3,…, 0<q<1, β>0. Its cumulative distribution function is F(x; q, β)=q^{x^{-β}}

## Value

`ddiweibull` gives the probability, `pdiweibull` gives the distribution function, `qdiweibull` gives the quantile function, and `rdiweibull` generates random values. See the reference below for the continuous inverse Weibull distribution.

## References

Dutang, C., Goulet, V., Pigeon, M. (2008) actuar: An R package for actuarial science, Journal of Statistical Software 25(7): 1-37

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```# Ex.1 x<-1:10 q<-0.6 beta<-0.8 ddiweibull(x, q, beta) t<-qdiweibull(0.99, q, beta) t pdiweibull(t, q, beta) # Ex.2 q<-0.4 beta<-1.7 n<-100 x<-rdiweibull(n, q, beta) tabulate(x)/sum(tabulate(x)) y<-1:round(max(x)) # compare with ddiweibull(y, q, beta) ```

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