The Extended Maximum Likelihood Estimation for Monotone Probability Mass Function with Application using Forensic Data

Abstract: This paper presents solutions to the modelling of frequency data of species labels, but the data is incomplete in the sense that some rarely-occurring species labels give zero observed frequency. The data can be modelled by a monotone probability function with parameters to be estimated, and yet, due to the order constraints and the incomplete data, using conventional parameter estimation methods will cause trouble. Therefore, we study a previously introduced method to resolve the issue. We begin with a brief tour through the attempts of parameter estimation, starting with the estimators which lead to problematic situations when using them. After that, we will study the improved estimation introduced in [1], which resolves the problem. The improved estimation method seems to perform well when dealing with the problem, and it may be especially useful in the fields of forensic science, zoology, medical science, business analytic and even several fields of machine learning.