Density (PDF), distribution function (CDF), and hazard function for Finite mixture of inverse Gaussian Distributions.
dmixinvgauss(x, theta = .2, lambda = .1, gamma = .05, forceExpectation = F)
pmixinvgauss(q, theta = .2, lambda = .1, gamma = .05, forceExpectation = F)
mixinvgaussHazard(x, theta = .2, lambda = .1, gamma = .05, forceExpectation = F)
vector of quantiles.
parameters, see 'Details'.
logical; if TRUE, the expectation of the distribution is forced to be 1..
The finite mixture of inverse Gaussian distributions was used by Gomes-Deniz and Perez-Rodrigues (201X) for ACD-models. Its PDF is:
$$f(x) = \frac{\gamma + x}{\gamma + \theta} \sqrt{\frac{\lambda}{2 \pi x^3}} \exp \left[ - \frac{\lambda(x-\theta)^2}{2 x \theta^2}\right].$$
If forceExpectation = TRUE the distribution is transformed by dividing the random variable with its expectation and using the change of variable function.
Gomez-Deniz Perez-Rodriguez (201X) Non-exponential mixtures, non-monotonic financial hazard functions and the autoregressive conditional duration model. Working paper. Retrieved June 16, 2015, from http://dea.uib.es/digitalAssets/254/254084_perez.pdf.