A new formulation of generalized gamma: Some results and applications

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-10-03 DOI:10.1051/ps/2023018

Cheng Peng

引用次数: 0

Abstract

We extend the 2-parameter Weibull to the generalized gamma distribution by adding a new partial parameter. The new shape parameter can be used to easily generate generalized gamma distributions with different shapes of the density function, hazard rate, and mean residual lifetimes that are useful in simulating various business processes such as manufacturing processes, and reliability systems. We derived some theoretical results and created visual presentations to demonstrate the behaviors of this new shape parameter as well. A new Monte Carlo simulation based on the new parameter was proposed to assess the discrepancy between the generalized gamma and its subfamilies. The power analysis of the proposed test was evaluated via simulation studies. We also present some numerical examples.

查看原文本刊更多论文

广义伽玛的一个新公式:一些结果和应用

通过增加一个新的偏参数，我们将2参数威布尔推广到广义伽玛分布。新的形状参数可以很容易地生成具有不同形状的密度函数、危险率和平均剩余寿命的广义伽马分布，这些分布在模拟各种业务过程(如制造过程和可靠性系统)中很有用。我们得到了一些理论结果，并创建了视觉演示来演示这个新的形状参数的行为。提出了一种基于新参数的蒙特卡罗模拟方法来评估广义伽玛及其子族之间的差异。通过仿真研究对所提出的试验的功率分析进行了评估。我们也给出了一些数值例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.