pcomposite {gendist} | R Documentation |
Cumulative distribution function of composite model.
Description
Computes cdf of the composite model.
Usage
pcomposite(q, spec1, arg1, spec2, arg2, initial = 1, lower.tail = TRUE, log.p = FALSE)
Arguments
q |
scalar or vector of values to compute the cdf. |
spec1 |
a character string specifying the head parent distribution (for example, "lnorm" if the parent distribution corresponds to the lognormal). |
arg1 |
list of arguments/parameters of the head parent distribution. |
spec2 |
a character string specifying the tail parent distribution (for example, "exp" if the parent distribution corresponds to the exponential). |
arg2 |
list of arguments/parameters of the tail parent distribution. |
initial |
initial values of the threshold, |
lower.tail |
logical; if |
log.p |
logical; if |
Details
The cdf of composite model has a general form of:
F(x) =
\frac{1}{1+\phi} \frac{F_{1}(x)}{F_{1}(\theta)} \mbox{ if } \quad x \leq \theta,
= \frac{1}{1+\phi} \left( 1 + \phi \frac{F_{2}(x)-F_{2}(\theta)}{1-F_{2}(\theta)} \right) \mbox{ if } \quad x > \theta,
whereby \phi
is the weight component, \theta
is the threshold and F_{i}(x)
for i=1,2
are the cdfs correspond to head and tail parent distributions, respectively.
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).
Cooray, K., & Ananda, M. M. (2005). Modeling actuarial data with a composite lognormal-Pareto model. Scandinavian Actuarial Journal, 2005(5), 321-334.
Scollnik, D. P. (2007). On composite lognormal-Pareto models. Scandinavian Actuarial Journal, 2007(1), 20-33.
Nadarajah, S., & Bakar, S. A. A. (2014). New composite models for the Danish fire insurance data. Scandinavian Actuarial Journal, 2014(2), 180-187.
Bakar, S. A., Hamzah, N. A., Maghsoudi, M., & Nadarajah, S. (2015). Modeling loss data using composite models. Insurance: Mathematics and Economics, 61, 146-154.
Examples
x=runif(10, min=0, max=1)
y=pcomposite(x, spec1="lnorm", arg1=list(meanlog=0.1,sdlog=0.2), spec2="exp",
arg2=list(rate=0.5) )