Discreetly mixed Q-Weibull and exponential {ACDm} R Documentation

## Discreet mix of the q-Weibull and the exponential distributions

### Description

Density (PDF), distribution function (CDF), and hazard function for a discreetly mixed distribution of the q-Weibull and the exponential distributions.

### Usage

dmixqwe(x, pdist = .5, a = .8, qdist = 1.5, lambda = .8, b = 1, forceExpectation = F)
pmixqwe(q, pdist = .5, a = .8, qdist = 1.5, lambda = .8, b = 1, forceExpectation = F)
mixqweHazard(x, pdist = .5, a = .8, qdist = 1.5, lambda = .8, b = 1, forceExpectation = F)

### Arguments

 x, q vector of quantiles. pdist, a, qdist, lambda, b parameters, see 'Details'. forceExpectation logical; if TRUE, the expectation of the distribution is forced to be 1 by letting b be a function of the other parameters.

### Details

The PDF for the mixed distribution is:

f(x) = p(2-q)\frac{a}{b^a} x^{a-1} ≤ft[1-(1-q)≤ft(\frac{x}{b}\right)^a\right]^{\frac{1}{1-q}} + (1-p)\frac{1}{λ}exp(-\frac{x}{λ})

if forceExpectation = TRUE the b parameter is a function of the other parameters to force the expectation to be 1.