ACDm (version 1.0.3)

Discreetly mixed Q-Weibull and ordinary Weibull: 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: $$f(x) = p(2-q)\frac{a}{b^a} x^{a-1} \left[1-(1-q)\left(\frac{x}{b}\right)^a\right]^{\frac{1}{1-q}} + (1-p)\theta \gamma x^{-\theta x^{\gamma}}$$ if forceExpectation = TRUE the b parameter is a function of the other parameters to force the expectation to be 1.

See Also

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