Estimation in the Three-Parameter Gamma Distribution Based on the Profile Log-Likelihood Function

Abstract

In this article, we express the profile log-likelihood function for the three-parameter gamma distribution in terms of the location parameter only and we study its properties. The behavior of the profile function is examined as the location parameter tends to the boundary values, i.e., to − ∞ and to the minimum value of the sample. As a result, we obtain that if the log-likelihood function has a local maximum then it has another stationary value which is a saddle point. The results are supported with the use of simulation results.

Keywords:

• Hessian matrix
• Maximum likelihood estimator
• Stationary value

Mathematics Subject Classification:

• Primary 62F10
• Secondary 62F99