Maximum Likelihood Estimates of Parameters in Generalized Gamma Distribution with SeLF Algorithm

TL;DR

This paper introduces a new method using the SeLF algorithm to efficiently and accurately estimate parameters in the generalized Gamma distribution, outperforming traditional methods in stability and speed.

Contribution

It develops a novel approach combining SeLF and US algorithms for maximum likelihood estimation in the generalized Gamma distribution, enhancing computational efficiency and accuracy.

Findings

SeLF algorithm achieves faster convergence than Newton's method.

The proposed method provides more stable and accurate parameter estimates.

Simulations demonstrate improved performance in practical data analysis.

Abstract

This undergraduate thesis focuses on calculating maximum likelihood estimates of parameters in the generalized Gamma distribution using the SeLF algorithm. As an extension of the Gamma distribution, the generalized Gamma distribution can better fit real data and has been widely applied. The research begins by exploring the definition of the generalized Gamma distribution and its similarities and differences from the traditional Gamma distribution. Then, the SeLF and US algorithms are discussed in detail. The SeLF algorithm is a new algorithm based on the Minorization-Maximization algorithm, which can obtain the local optimal solution with few iterations, with the advantages of fast computation, high accuracy, and good convergence. The US algorithm is a method for finding the zeros of a function, which stands at a higher level than the SeLF algorithm and can improve the convergence speed and stability. This thesis proposes a method for calculating maximum likelihood estimates of the parameters in the generalized Gamma distribution using the SeLF and US algorithms, and presents the practical implementation of the algorithms, as well as simulations and data analysis to evaluate the performance of the proposed methods. The results demonstrate that the SeLF algorithm can achieve more stable and accurate estimates of the parameters in the generalized Gamma distribution more quickly, compared to traditional Newton's method, which can be useful in various applications. This thesis provides a comprehensive and in-depth exploration of the generalized Gamma distribution and the SeLF algorithm, and proposes a new method for calculating maximum likelihood estimates of parameters, contributing to the development of statistical methods for parameter estimation in complex models. The proposed method in this thesis has important practical significance and application value for solving practical problems.