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.

翻译：本本科毕业论文聚焦于利用SeLF算法计算广义Gamma分布的参数极大似然估计。作为Gamma分布的扩展，广义Gamma分布能更好地拟合实际数据，并已得到广泛应用。研究首先探讨了广义Gamma分布的定义及其与传统Gamma分布的异同。随后，详细讨论了SeLF算法与US算法。SeLF算法是一种基于Minorization-Maximization算法的新算法，能以较少迭代次数获得局部最优解，具有计算速度快、精度高、收敛性好的优点。US算法是一种求函数零点的方法，其层次高于SeLF算法，能够提升收敛速度与稳定性。本文提出了一种利用SeLF与US算法计算广义Gamma分布参数极大似然估计的方法，给出了算法的具体实现，并通过仿真与数据分析评估了所提方法的性能。结果表明，相较于传统的牛顿法，SeLF算法能够更快、更稳定且更准确地估计广义Gamma分布的参数，这可在多种应用场景中发挥作用。本文对广义Gamma分布与SeLF算法进行了全面深入的探讨，并提出了一种新的参数极大似然估计计算方法，为复杂模型参数估计的统计方法发展做出了贡献。本文所提方法对于解决实际问题具有重要的现实意义与应用价值。