Simulation of truncated and unimodal gamma distributions

IF 1.1 4区数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Statistical Computation and Simulation Pub Date : 2023-11-07 DOI:10.1080/00949655.2023.2277339

Yuta Kurose

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引用次数: 0

Abstract

AbstractAn efficient random variable generator for a truncated gamma distribution with shape parameter greater than 1 is designed using an acceptance-rejection algorithm. Based on an approximation to a transformed gamma density function by the standard normal density, numerical information for the standard normal density is prepared in advance, and the calculation is performed with reference to that information. An improvement via a squeezing method is proposed to reduce the computational burden and time. The algorithm's acceptance rate for generating truncated gamma variables is very high and almost 1 when the truncated distribution is unimodal. Numerical experiments for one- and two-sided truncated domain cases are conducted to measure the execution time, including the parameter setup time. Compared with existing truncated gamma variate generators, the proposed method performs better when the distribution is unimodal and the shape parameter is equal to or greater than 3.3.Keywords: Acceptance-rejection algorithmshape parametersqueezingtruncated gamma distributionMathematics Subject Classifications: 65C0565C1062-08 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research was supported by JSPS KAKENHI Grant Numbers JP19H00588 and JP20K19751.

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截断和单峰伽马分布的模拟

摘要针对形状参数大于1的截断分布，采用接受-拒绝算法设计了一种高效的随机变量生成器。基于标准正态密度对变换后的伽马密度函数的近似，预先准备好标准正态密度的数值信息，并参照该信息进行计算。为了减少计算量和时间，提出了一种通过挤压法的改进方法。该算法对截断分布的接受率非常高，当截断分布为单峰分布时，接受率几乎为1。对单侧和双侧截断域情况进行了数值实验，测量了包括参数设置时间在内的执行时间。与现有的截断伽马变量生成器相比，当分布为单峰且形状参数等于或大于3.3时，该方法具有更好的性能。关键词:接受-拒绝算法形状参数压缩截断伽马分布数学学科分类:65C0565C1062-08披露声明作者未报告潜在利益冲突。本研究得到了JSPS KAKENHI基金号JP19H00588和JP20K19751的支持。

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来源期刊

Journal of Statistical Computation and Simulation 数学-计算机：跨学科应用

CiteScore

2.30

自引率

8.30%

发文量

156

审稿时长

4-8 weeks

期刊介绍： Journal of Statistical Computation and Simulation ( JSCS ) publishes significant and original work in areas of statistics which are related to or dependent upon the computer. Fields covered include computer algorithms related to probability or statistics, studies in statistical inference by means of simulation techniques, and implementation of interactive statistical systems. JSCS does not consider applications of statistics to other fields, except as illustrations of the use of the original statistics presented. Accepted papers should ideally appeal to a wide audience of statisticians and provoke real applications of theoretical constructions.