A Linear Immigration-Birth-Death Model and Its Statistical Inference

ZHANG Shu-lin, WEI Zheng-hong, BI Qiu-xiang

doi:10.13371/j.cnki.chin.q.j.m.2014.03.005

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 3: 356 - 362

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.03.005

A Linear Immigration-Birth-Death Model and Its Statistical Inference

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1. School of Statistics, Southwestern University of Finance and Economics2. College of Mathematics and Computational Science, University of Shenzhen3. Department of Fixed Income GF Securities, Company Limited

ZHANG Shu-lin(1976-), male, native of Chengdu, Sichuan, a lecturer of Southwestern University of Finance and Economics University, Ph.D., engages in statistics; WEI Zheng-hong(1964-), female, native of Shenzhen, Guangdong, a professor of University of Shenzhen, Ph,D., engages in statistics; BI Qiu-xiang(1964-), female, native of Guangzhou, Guangdong, a manager of GF Securities, Company Limited, Ph,D., engages in statistics.

Received date: 2012-01-25

Online published: 2020-11-30

Supported by

Supported by the Fundamental Research Funds for the Central Universities(JBK120405)；

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Abstract

In this paper, we employ moment generating function to obtain some exact formula of transition probability of immigration-birth-death（IBD） model and discuss the simulation of sample path and statistical inference with complete observations of the IBD process by the exact transition density formula.

Key words： immigration-birth-death process; transition density; moment generating function; maximum likelihood estimator

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ZHANG Shu-lin, WEI Zheng-hong, BI Qiu-xiang . A Linear Immigration-Birth-Death Model and Its Statistical Inference[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(3) : 356 -362 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.03.005

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