Moment estimation for the mixture of two exponential distributions

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".

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.

Author

Yves Deville

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.

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)