Simple estimation for the mixture of two exponential distributions

Compute a simple (preliminary) estimation for the tree parameters of the mixture of two exponential distributions

Usage

ini.mixexp2(x, plot = FALSE)

Arguments

x

Sample: numerical vector with elements >0.

plot

Should a graphic be displayed?

Details

This function gives estimators using several methods if necessary. The goal is to find the rates rate1, rate2 and the mixing probability prob1 with the 'feasibility' constraints 0 < rate1 < rate2 and 0 < prob1 < 1.

First the method of moments is used. If the estimates are feasible they are returned with method = "moments". If not, the estimates are derived using two linear regressions. A regression without constant using only the smallest values gives an estimator of the mean rate. A regression using only the largest values gives rate1 and prob1. Yet the constraints must be fulfilled. If they are, the estimates are returned (together with method = "Hreg" suggesting a cumulative hazard regression). If not, a (poor) default estimate is returned with method = "arbitrary".

Value

A list

estimate

A vector with named elements "prob1", "rate1" and "rate2".

method

The method that really produced the estimators.

Author

Yves Deville

Note

The method of moments is implemented in mom.mixexp2. Further investigations are needed to compare the estimators (moments or Hreg) and select the best strategy.

Note that this function returns the estimate within a list and no longer as a vector with named elements as was the case before.

Examples

set.seed(1234)
x <- rmixexp2(n = 100, prob1 = 0.5, rate2 = 4)
res <- ini.mixexp2(x, plot = TRUE)