mapfit (version 0.9.6)

herlang: Hyper-Erlang Distribution

Description

Density function, distribution function and random generation for the hyper-Erlang distribution, and a function to generate an object of herlang.

Usage

herlang(shape, mixrate = rep(1/length(shape), length(shape)),
	     rate = rep(1, length(shape)))
dherlang(x, herlang = herlang(shape = c(1)), log = FALSE)
pherlang(q, herlang = herlang(shape = c(1)), lower.tail = TRUE, log.p = FALSE)
rherlang(n, herlang = herlang(shape = c(1)))

Value

herlang gives an object of hyper-Erlang distribution. dherlang gives the density function, pherlang gives the distribution function, and rherlang generates random samples.

Details

The hyper-Erlang distribution with parameters $mixrate$, $shape$ and $rate$: Cumulative probability function; $$F(q) = \sum_i \int_0^q maxirate_i rate_i^shape_i x^(shape_i-1) e^(-rate_i x) / (shape_i - 1)! dx$$ Probability density function; $$f(x) = \sum_i maxirate_i rate_i^shape_i x^(shape_i-1) e^(-rate_i x) / (shape_i - 1)!$$

See Also

ph, herlang

Examples

## create a hyper Erlang consisting of two Erlang
## with shape parameters 2 and 3.
(param1 <- herlang(c(2,3)))

## create a hyper Erlang consisting of two Erlang
## with shape parameters 2 and 3.
(param1 <- herlang(shape=c(2,3)))

## create a hyper Erlang with specific parameters
(param2 <- herlang(shape=c(2,3), mixrate=c(0.3,0.7),
	               rate=c(1.0,10.0)))

## convert to a general PH
as(param2, "ph")

## p.d.f. for 0, 0.1, ..., 1
(dherlang(x=seq(0, 1, 0.1), herlang=param2))

## c.d.f. for 0, 0.1, ..., 1
(pherlang(q=seq(0, 1, 0.1), herlang=param2))

## generate 10 samples
(rherlang(n=10, herlang=param2))