qWeibullDist: The q-Weibull distribution

In ACDm: Tools for Autoregressive Conditional Duration Models

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.

ACDm documentation built on May 29, 2024, 12:04 p.m.