gendist (version 2.0)

dcomposite: Probabilty density function of composite model.

Description

Computes pdf of the composite model.

Usage

dcomposite(x, spec1, arg1, spec2, arg2, initial = 1, log = FALSE)

Arguments

x

scalar or vector of values to compute the pdf.

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, \(\theta\).

log

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

Value

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

Details

The pdf of composite model has a general form of: $$ f(x) = \frac{1}{1+\phi} f_{1}^{*}(x), \mbox{ if} \quad x \leq \theta, $$ $$ = \frac{\phi}{1+\phi} f_{2}^{*}(x), \mbox{ if} \quad x > \theta, $$ whereby \(\phi\) is the weight component, \(\theta\) is the threshold and \(f_{i}^{*}(x)\) for \(i=1,2\) are the truncated pdfs correspond to head and tail parent distributions defined by $$ f_{1}^{*}(x) = \frac{f_{1}(x)}{F_{1}(\theta)} $$ and $$ f_{2}^{*}(x) = \frac{f_{2}(x)}{1-F_{2}(\theta)} $$ 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=dcomposite(x, spec1="lnorm", arg1=list(meanlog=0.1,sdlog=0.2), spec2="exp", 
             arg2=list(rate=0.5) )
# }