PARAMETER ESTIMATION FOR GAMMA DISTRIBUTIONS BY MOMENT GENERATING FUNCTIONS IN THE PRESENCE OF OUTLIERS

Abstract

The presence of outliers within datasets can significantly alter their behavior, leading to substantial errors in estimated results. Consequently, accurate parameter estimation necessitates the identification and mitigation of outlier effects. Various methodologies, including Method of Moments Estimation (MME) and Maximum Likelihood Estimation (MLE), are employed to estimate parameters in distributions affected by outliers. This research explores the dynamic behavior of parameters in the presence of outliers and devises strategies to mitigate their influence. Emphasis is placed on understanding the multifaceted impact of outliers on data sets, including their potential to distort formulas, mischaracterize parameters, and skew summary statistics. A simulated study is conducted to assess the robustness of test statistics in outlier detection. The Gamma distribution is examined, particularly in the context of size-biased and area-biased functions, with parameters calculated accordingly. Discordancy tests are employed to identify outliers, with graphical representations aiding in the delineation of scale and shape parameter behaviors. Furthermore, this research extends to the detection and analysis of both single and dual outliers, facilitating a comprehensive understanding of their effects and subsequent recalibration of results.