Description Usage Arguments Details Value Author(s) References See Also Examples
Density function for the Coxian distribution with index vector equal to probvec
and rate vector equal to lambdvec
.
1 |
x |
vector of positions. |
probvec |
index vector |
lambdvec |
rate vector |
log |
logical; if TRUE, density d are given as log(d) |
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. dcox
provides with density function of Coxian distributions by using the method of [1].
dcox
gives the density function.
The length of the result is the length of x
.
Only the first elements of the logical arguments are used.
Junrong Liu
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]
Distributions
for other standard distribution
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