  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.
