# qWeibullDist: The q-Weibull distribution In ACDm: Tools for Autoregressive Conditional Duration Models

 qWeibullDist R Documentation

## 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(ε) = (2-q)\frac{a}{b^a} ε^{a-1} ≤ft[1-(1-q)≤ft(\frac{ε}{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 Nov. 16, 2022, 5:09 p.m.