﻿ 一种新的系统寿命分布—混合指数泊松分布 A New Lifetime Distribution of System—Mixture Exponential Poisson Distribution

Statistical and Application
Vol.04 No.04(2015), Article ID:16682,7 pages
10.12677/SA.2015.44032

A New Lifetime Distribution of System

—Mixture Exponential Poisson Distribution

Dongli Cui, Weiyan Mu

School of Science, Beijing University of Civil Engineering and Architecture, Beijing

Received: Dec. 9th, 2015; accepted: Dec. 27th, 2015; published: Dec. 30th, 2015

Copyright © 2015 by authors and Hans Publishers Inc.

ABSTRACT

Lifetime distribution is a class of important matters in statistics, the parameter model of the lifetime distribution has the advantages of the mature theory, the simple calculation and the strong operation in practice. Therefore, we define a new lifetime distribution of system—the mixture exponential Poisson distribution based on the condition of the lifetime of the components and the number of the components subject to double parameters mixture exponential distribution and Poisson distribution, respectively. As a statistical model, we studied the various properties of the distribution, and discussed the maximum likelihood estimation of parameters under the condition of censored data of fixed number and time in this paper.

Keywords:Mixture Exponential Poisson Distribution, Maximum Likelihood Estimation, Lifetime Distribution

—混合指数泊松分布

1. 引言

2. 混合指数泊松分布的定义

，所以X的边缘分布函数为

(1)

X的边缘密度函数为

(2)

3. 混合指数泊松分布的性质

3.1. 密度函数的单调性

3.2. 分位数

3.3. 期望与方差

，则，根据泰勒公式，可以得到

，则，所以最终把转化为求M。而

3.4. 生存函数与风险函数

1) 生存函数（或可靠度函数）为 [6]

2) 风险函数为 [7]

4. 混合指数泊松分布下的参数估计

4.1. 定数截尾数据下对参数的估计

，所以似然函数为

4.2. 定时截尾数据下对参数的估计

A New Lifetime Distribution of System—Mixture Exponential Poisson Distribution[J]. 统计学与应用, 2015, 04(04): 289-295. http://dx.doi.org/10.12677/SA.2015.44032

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