Probabilty density function of arc tan model.

Description

Computes pdf of the arc tan model.

Usage

1
darctan(x, alpha, spec, arg, log = FALSE)

Arguments

x

scalar or vector of values to compute the pdf.

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.

log

logical; if TRUE, log(pdf) are returned.

Details

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

f(x) = \frac{1}{\arctan(α)} \frac{α g(x)}{1 + (α (1-G(x)))^{2}}

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

Value

An object of the same length as x, giving the pdf values computed at x.

Author(s)

Shaiful Anuar Abu Bakar

References

S.A. Abu Bakar, S. Nadarajah, Z.A. ABSL Kamarul Adzhar, I. Mohamed. gendist: An R package for generated probability distribution models, submitted.
Gomez-Deniz, E., & Calderin-Ojeda, E. Modelling insurance data with the pareto arctan distribution. ASTIN Bulletin, 1-22.

Examples

1
2
x=runif(10, min=0, max=1)
y=darctan(x, alpha=0.5, spec="lnorm", arg=list(meanlog=1,sdlog=2) )