parctan: Cumulative distribution function of arc tan model.
In gendist: Generated Probability Distribution Models

Description Usage Arguments Details Value Author(s) References Examples

Computes cdf of the arc tan model.

1	parctan(q, alpha, spec, arg, lower.tail = TRUE, log.p = FALSE)

`q`	scalar or vector of values to compute the cdf.
`alpha`	the value of α parameter, α>0.
`spec`	a character string specifying the parent distribution (for example, "lnorm" if the parent distribution corresponds to the lognormal).
`arg`	list of arguments/parameters of the parent distribution.
`lower.tail`	logical; if `TRUE`, cdf are returned, otherwise 1-cdf.
`log.p`	logical; if `TRUE`, probabilities returned are given as log(cdf).

The cdf of arc tan model with parameter α has a general form of:

F(q) = 1- \frac{\arctan(α (1-G(q)) )}{\arctan(α)}

for a≤q x≤q b where a and b follow the support of g(q). \arctan denote the inverse function of tangent. g(q) and G(q) are the pdf and cdf of parent distribution, respectively. Note also that α>0.

An object of the same length as q, giving the cdf values computed at q.

Shaiful Anuar Abu Bakar

Abu Bakar, S. A., Nadarajah, S., Adzhar, Z. A. A. K., & Mohamed, I. (2016). gendist: An R package for generated probability distribution models. PloS one, 11(6).
Gomez-Deniz, E., & Calderin-Ojeda, E. Modelling insurance data with the pareto arctan distribution. ASTIN Bulletin, 1-22.