ph: Phase-Type (PH) Distribution In mapfit: A Tool for PH/MAP Parameter Estimation

Description

Density function, distribution function and random generation for the PH distribution, and a function to generate an object of `ph`.

Usage

 ```1 2 3 4``` ```ph(size, alpha, Q, xi, class = "CsparseMatrix") dph(x, ph = ph(1), log = FALSE) pph(q, ph = ph(1), lower.tail = TRUE, log.p = FALSE) rph(n, ph = ph(1)) ```

Arguments

 `size` a value for the number of phases. `alpha` a vector for the initial probabilities of PH distribution. `Q` an object of Matrix class for the initesmal generator of PH distribution. `xi` a vector for the exit rates of PH distribution. `class` name of Matrix class for `Q`. `x, q` vectors of quantiles. `p` a vector of probabilities. `n` number of observations. `ph` an object of S4 class of PH (`ph`). `log` logical; if `TRUE`, the log density is returned. `lower.tail` logical; if `TRUE`, probabilities are P[X <= x], otherwise, P[X > x]. `log.p` logical; if `TRUE`, the log probability is returned.

Details

The PH distribution with parameters α, Q and ξ: Cumulative probability function;

F(q) = 1 - α \exp( Q q ) 1

Probability density function;

f(x) = α \exp( Q x ) ξ

Value

`ph` gives an object of general PH distribution. `dph` gives the density function, `pph` gives the distribution function, and `rph` generates random samples.

Note

`ph` requires either `size` or (`alpha`, `Q`, `xi`). `rph` for `ph` is too slow. It is recommended to use `rph` for `cf1`.

`cf1`, `herlang`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## create a PH (full matrix) with 5 phases (param1 <- ph(5)) ## create a PH (full matrix) with 5 phases (param1 <- ph(size=5)) ## create a PH with specific parameters (param2 <- ph(alpha=c(1,0,0), Q=rbind(c(-4,2,0),c(2,-5,1),c(1,0,-1)), xi=c(2,2,0))) ## p.d.f. for 0, 0.1, ..., 1 (dph(x=seq(0, 1, 0.1), ph=param2)) ## c.d.f. for 0, 0.1, ..., 1 (pph(q=seq(0, 1, 0.1), ph=param2)) ## generate 10 samples (rph(n=10, ph=param2)) ```