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

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

### Description

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

### Usage

dmixqww(x, pdist = .5, a = 1.2, qdist = 1.5, theta = .8, gamma = 1, b = 1,
forceExpectation = F)

pmixqww(q, pdist = .5, a = 1.2, qdist = 1.5, theta = .8, gamma = 1, b = 1,
forceExpectation = F)

mixqwwHazard(x, pdist = .5, a = 1.2, qdist = 1.5, theta = .8, gamma = 1, b = 1,
forceExpectation = F)


### Arguments

 x, q vector of quantiles. pdist, a, qdist, theta, gamma, 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)θ γ x^{-θ x^{γ}}

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

qWeibullDist for the Q-Weibull distribution and pmixqwe for Q-Weibull mixed with the exponential distribution.