phfit.3mom {mapfit}

PH fitting with three moments

Description

Estimates PH parameters from three moments.

Usage

phfit.3mom(
  m1,
  m2,
  m3,
  method = c("Osogami06", "Bobbio05"),
  max.phase = 50,
  epsilon = sqrt(.Machine$double.eps)
)

Arguments

m1

A value of the first moment.

m2

A value of the second moment.

m3

A value of the third moment.

method

The name of moment matching method.

max.phase

An integer for the maximum number of phases in the method "Osogami06".

epsilon

A value of precision in the method "Osogami06".

Value

An object of GPH.

Note

The method "Osogami06" checks the first three moments on whether there exists a PH whose three moments match to them. In such case, the method "Bobbio05" often returns an error.

References

Osogami, T. and Harchol-Balter, M. (2006) Closed Form Solutions for Mapping General Distributions to Minimal PH Distributions. Performance Evaluation, 63(6), 524–552.

Bobbio, A., Horvath, A. and Telek, M. (2005) Matching Three Moments with Minimal Acyclic Phase Type Distributions. Stochastic Models, 21(2-3), 303–326.

Examples

## Three moment matching
## Moments of Weibull(shape=2, scale=1); (0.886227, 1.0, 1.32934)
(result1 <- phfit.3mom(0.886227, 1.0, 1.32934))

## Three moment matching
## Moments of Weibull(shape=2, scale=1); (0.886227, 1.0, 1.32934)
(result2 <- phfit.3mom(0.886227, 1.0, 1.32934, method="Bobbio05"))

## mean
ph.mean(result1)
ph.mean(result2)

## variance
ph.var(result1)
ph.var(result2)

## up to 5 moments 
ph.moment(5, result1)
ph.moment(5, result2)