pcox: Distribution function for Coxian distributions.

In dpqrcox: The `dpqrcox' package provides d/p/q/r functions of Coxian distributions.

Description

Distribution function for the Coxian distribution with index vector equal to probvec and rate vector equal to lambdvec.

Usage

pcox(x, probvec, lambdvec, lower.tail = TRUE, log.p = FALSE)

Arguments

x	vector of positions.
probvec	index vector
lambdvec	rate vector
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x]
log.p	logical; if TRUE, probabilities p are given as log(p).

Details

Assume that X_1, ..., X_n be independent exponential random variables with respective rates λ_1, ..., λ_n. Assume that P(I=i)=p_i, i=1, ..., n and the be random variable I is independent of X_1, ..., X_n. Then the random variable

X=X_1+…+X_I

is a Coxian random variable with index vector probvec=(p_1,…,p_n) and rate vector lambdvec=(λ_1,…,λ_n).

The probability distribution of a Coxian random variable is a mixture of convolutions of exponential distributions. A Coxian distribution can approximate any positive-valued distribution. However, approximations is poor sometimes. [1] indicated that numerical error in computing density and probability functions is one of reasons for the issue. pcox provides with distribution function of Coxian distributions by using the method of [1].

Value

pcox gives the probability function.

The length of the result is the length of x.

Only the first elements of the logical arguments are used.

Author(s)

Junrong Liu

References

Qihong Duan and Junrong Liu. (2016), Modelling a Bathtub-Shaped Failure Rate by a Coxian Distribution, IEEE TRANSACTIONS ON RELIABILITY 65(2), pp.878-885. DOI: 10.1109/TR.2015.2494374 [1]

See Also

Distributions for other standard distribution

dpqrcox documentation built on May 2, 2019, 4:56 p.m.