mom.mixexp2: Moment estimation for the mixture of two exponential...

In Renext: Renewal Method for Extreme Values Extrapolation

Moment estimation for the mixture of two exponential distributions

Description

Compute the moment estimation for the tree parameters of the mixture of two exponential distributions

Usage

   mom.mixexp2(x)

Arguments

x	Sample. Vector containing values >0.

Details

The three parameters (probability and the two rates) are computed from the first three moments (theoretical and sample). It can be shown that the inverse rates are obtained solving a quadratic equation. However the roots can be negative or complex and the estimates are not valid ones.

Value

A list with elements

estimate	A vector with named elements "prob1", "rate1" and "rate2". When the moment estimators are not valid (negative or complex rates), a vector of three NA is returned.
method	Character "moments".

Note

The theoretical coefficient of variation (CV) of a mixture of two exponential distributions always exceeds 100%. When the sample CV is smallest than 100%, no valid estimates exist since the two first moments can not be matched.

Author(s)

Yves Deville

References

Paul R. Rider. The Method of Moments Applied to a Mixture of Two Exponential Distributions. Ann. Math. Statist. Vol. 32, Number 1 (1961), 143-147.

See Also

See ini.mixexp2 for a more versatile initial estimation.

Examples

x <- rmixexp2(n = 100, prob1 = 0.5, rate1 = 1.0, rate2 = 3.0)
est <- mom.mixexp2(x)

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