parctan {gendist} | R Documentation |
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 |
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 |
log.p |
logical; if |
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
.
Value
An object of the same length as q
, giving the cdf values computed at q
.
Author(s)
Shaiful Anuar Abu Bakar
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
x=runif(10, min=0, max=1)
y=parctan(x, alpha=0.5, spec="lnorm", arg=list(meanlog=1,sdlog=2) )