指数威布尔更新函数的近似计算

程从华

doi:10.13371/j.cnki.chin.q.j.m.2018.04.002

数学季刊 >

2018 , Vol. 33 >Issue 4: 341 - 357

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.04.002

指数威布尔更新函数的近似计算

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School of Mathematics and Statistics, Zhaoqing University

CHENG Cong-hua, Male, Sichuan, Associate Professor, Research area: Survival analysis and empirical likelihood.

录用日期: 2016-12-18

网络出版日期: 2020-10-07

基金资助

supported by the National Natural Science Foundation of China(71801186)； the National Natural Science Foundation of Guangdong(2018A030313829)； the Science and Technology Innovation Guidance Project of Zhaoqing,Guangdong Province(201804031503)； the higher education colleges and universities innovation strong school project of Guangdong(2016KTSCX153)； the teaching reform project of Zhaoqing University(zlgc201745)；

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The Approximation of the Exponential Weibull Renewal Function

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School of Mathematics and Statistics, Zhaoqing University

CHENG Cong-hua, Male, Sichuan, Associate Professor, Research area: Survival analysis and empirical likelihood.

Accepted date: 2016-12-18

Online published: 2020-10-07

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摘要

The analytical renewal function(RF) is not tractable of the exponential Weibull(EW) distribution. In the proposed model, the n-fold convolution of the EW cumulative distribution function(CDF) is approximated by a n-fold convolutions of Gamma and normal CDFs. We obtain the EW RF by a series approximation model. The method is very simple in the computation. When the parameters are unknown, we present the asymptotic confidence interval of the RF. The validity of the asymptotic confidence interval is checked via some numerical experiments.

关键词： Renewal function; EW distribution; Gamma distribution; Normal distribution; Series truncation approximation

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程从华 . 指数威布尔更新函数的近似计算[J]. 数学季刊, 2018 , 33(4) : 341 -357 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.04.002

Abstract

Key words： Renewal function; EW distribution; Gamma distribution; Normal distribution; Series truncation approximation

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