qWeibullDist {ACDm}

The q-Weibull distribution

Description

Density (PDF), distribution function (CDF), quantile function (inverted CDF), random generation, exepcted value, and hazard function for the q-Weibull distribution.

Usage

dqweibull(x, a = .8, qdist = 1.2, b = 1, forceExpectation = F)
pqweibull(q, a = .8, qdist = 1.2, b = 1, forceExpectation = F)
qqweibull(p, a = .8, qdist = 1.2, b = 1, forceExpectation = F)
rqweibull(n = 1, a = .8, qdist = 1.2, b = 1, forceExpectation = F)
qweibullExpectation(a = .8, qdist = 1.2, b = 1)
qweibullHazard(x, a = .8, qdist = 1.2, b = 1, forceExpectation = F)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

a, qdist, 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 q-Weibull distribution is:

f(\epsilon) = (2-q)\frac{a}{b^a} \epsilon^{a-1} \left[1-(1-q)\left(\frac{\epsilon}{b}\right)^a\right]^{\frac{1}{1-q}}

The distribution was used for ACD models by Vuorenmaa (2009).

References

Vuorenmaa, T. (2009) A q-Weibull Autoregressive Conditional Duration Model with an Application to NYSE and HSE data. Available at SSRN: http://ssrn.com/abstract=1952550.