qcomposite {gendist}

Quantile function of composite model.

Description

Computes qf of the composite model.

Usage

qcomposite(p, spec1, arg1, spec2, arg2, initial = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

p

scalar or vector of probabilities to compute the qf.

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, probabilities are p, otherwise 1-p.

log.p

logical; if TRUE, probabilities p are returned as log(p).

Details

The qf of composite model has a general form of:

Q(p) = Q_{1}(p(1+\phi)F_{1}(\theta)) \mbox{ if } \quad p \leq \frac{1}{1+\phi},

= Q_{2} \left( F_{2}(\theta) + (1-F_{2}(\theta)) \left( \frac{p(1+\phi)-1}{\phi} \right)\right) \mbox{ if } \quad p > \frac{1}{1+\phi}

whereby \phi is the weight component, \theta is the threshold and F_{i}(x) for i=1,2 are the qfs correspond to head and tail parent distributions, respectively.

Value

An object of the same length as p, giving the qf values computed at p.

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=qcomposite(x, spec1="lnorm", arg1=list(meanlog=0.1,sdlog=0.2), spec2="exp", 
             arg2=list(rate=0.5) )