gendist (version 2.0)

pcomposite: 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, \(\theta\).

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 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.

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

# NOT RUN {
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) )
# }