EM.mixexp: Expectation-Maximisation for a mixture of exponential...

In Renext: Renewal Method for Extreme Values Extrapolation

Expectation-Maximisation for a mixture of exponential distributions

Description

Experimental function for Expectation-Maximisation (EM) estimation

Usage

EM.mixexp(x, m = 2)

Arguments

x	Sample vector with values >0.
m	Number of mixture components.

Details

The EM algorithm is very simple for exponential mixtures (as well as for many other mixture models).

According to a general feature of EM, this iterative method leads to successive estimates with increasing likelihood but which may converge to a local maximum of the likelihood.

Value

List with

estimate	Estimated values as a named vector.
logL	Vector giving the log-likelihood for successive iterations.
Alpha	Matrix with m columns giving probability weights for successive iterations. Row with number it contains the m probabilities at iteration it.
Theta	Matrix with m columns giving the estimates of the m expectations for the successive iterations

Note

The estimation is done for expectation (inverse rates) but the estimate vector in the result contains rates for compatibility reasons (e.g with exponential).

Author(s)

Yves Deville

See Also

mom.mixexp2 and ini.mixexp2 for "cheap" estimators when m = 2.

Examples

set.seed(1234)
x <- rmixexp2(n = 100, prob1 = 0.5, rate2 = 4)
EM.mixexp(x) -> res
res$estimate
matplot(res$Theta, type = "l", lwd = 2,
        xlab = "iteration", ylab = "theta",
        main = "exponential inverse rates")

Renext documentation built on Aug. 30, 2023, 1:06 a.m.