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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2014, Vol. 29 Issue (2): 138-146    DOI:
    
Marshall-Olkin extended distribution based on truncated Poisson distribution
ZHANG Ying-ying1, ZHANG Yi2,1
1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2. Central University of Finance and Economics, Beijing 100081, China
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Abstract  Through compound distributions, a parameter λ is introduced to expand a family of distributions . It has been shown that ageing property DFR is transmitted from one random variable to the new one. In addition, the closure of this model under different stochastic orders viz. likelihood ratio order, shifted likelihood ratio orders and shifted hazard rate orders is discussed. Also, this method is applied to exponential distribution and Log-normal distribution. Finally, application of the extended distribution to a data set representing the remission times of bladder cancer patients is given and its goodness-of-fit is demonstrated.

Key words： zero truncated poisson distribution      hazard rate function      exponential distribution      log-normal distribution      decreasing failure rate      stochastic orders      maximum likelihood estimation     
Received: 19 July 2013      Published: 28 July 2018
CLC:  O211.3  
  O212  
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Cite this article:

ZHANG Ying-ying, ZHANG Yi. Marshall-Olkin extended distribution based on truncated Poisson distribution. Applied Mathematics A Journal of Chinese Universities, 2014, 29(2): 138-146.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2014/V29/I2/138


基于截断Poisson分布的Marshall-Olkin拓展分布

采用复合分布的方法, 将一个参数$\lambda$和一个已有分布组合成一个新的分布的方法, 研究新分布与原分布之间的DFR的继承性和似然序关系. 在原分布分别取为指数分布和正态分布时, 分析其密度函数和危险率函数的等统计特征. 最后, 用一组数据进行实证研究, 利用极大似然估计估计出参数, 分别用指数扩展分布和指数分布拟合进行比较.

关键词： 零截断Poisson分布,  危险率函数,  指数分布,  正态分布,  DFR,  随机序,  极大似然估计 
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