Estimating the minimum and maximum location parameters for two gamma-exponential scale mixtures

Abstract

Suppose we have two components, each having a two-parameter exponential distribution. Suppose further that the components are conditionally independent with a random hazard rate and unequal, unknown, fixed location parameters. The objective of this paper is to estimate the minimum and maximum of the location parameters from conditionally independent samples taken from the mixed population. Several estimators are proposed and their properties in terms of MSE and absolute bias will be studied and compared. Interestingly, the relationships between these estimators always hold regardless of the mixing parameters assumed in the model.

Keywords:

• Maximum likelihood estimator
• absolute bias
• mean squared error
• hazard rate
• random environment