gendist (version 2.0)

parctan: Cumulative distribution function of arc tan model.

Description

Computes cdf of the arc tan model.

Usage

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

Arguments

q

scalar or vector of values to compute the cdf.

alpha

the value of \(\alpha\) parameter, \(\alpha>0\).

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).

Value

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

Details

The cdf of arc tan model with parameter \(\alpha\) has a general form of: $$ F(q) = 1- \frac{\arctan(\alpha (1-G(q)) )}{\arctan(\alpha)} $$ for \(a\leq x\leq b\) 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 \(\alpha>0\).

References

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.

Examples

# NOT RUN {
x=runif(10, min=0, max=1)
y=parctan(x, alpha=0.5, spec="lnorm", arg=list(meanlog=1,sdlog=2) )
# }