gendist (version 2.0)

pmixt: Cumulative distribution function of mixture model.

Description

Computes cdf of the mixture model.

Usage

pmixt(q, phi, spec1, arg1, spec2, arg2, lower.tail = TRUE, log.p = FALSE)

Arguments

q

scalar or vector of values to compute the cdf.

phi

the value of \(\phi\) parameter, \(\phi>0\).

spec1

a character string specifying the first parent distribution (for example, "lnorm" if the parent distribution corresponds to the lognormal).

arg1

list of arguments/parameters of the first parent distribution.

spec2

a character string specifying the second parent distribution (for example, "exp" if the parent distribution corresponds to the exponential).

arg2

list of arguments/parameters of the second parent distribution.

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 mixture model has a general form of: $$ F(x) = \\frac{1}{1+\phi} \left(G_{1}(x) + \phi G_{2}(x) \right) $$ where \(x\) follows the support of parent distributions, \(\phi\) is the weight component and \(G_{i}(x)\) for \(i=1,2\) are the cdfs of first and second 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). Pearson, K. (1894). Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London. A, 71-110.

Examples

# NOT RUN {
x=runif(10, min=0, max=1)
y=pmixt(x, phi=0.5, spec1="lnorm", arg1=list(meanlog=1,sdlog=2), spec2="exp", 
        arg2=list(rate=2) )
# }