复合负二项分布作为拉普拉斯分布和的无穷可除性

IF 1.1 Q3 STATISTICS & PROBABILITY

Pakistan Journal of Statistics and Operation Research Pub Date : 2022-06-01 DOI:10.18187/pjsor.v18i2.2767

D. Devianto, Stefi Amalia Fitri, Hazmira Yoza, M. Maiyastri

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引用次数: 0

摘要

复合负二项分布的无限可整除性，特别是拉普拉斯分布的和，对基于其特征函数的数学模型的控制具有重要作用。为了证明该复合负二项分布的特征函数性质，首先利用Fourier-Stieltjes变换使其具有特征函数，然后用解析方法对其连续性和二次型进行控制。通过引入满足特征函数条件的函数，使其卷积具有复合负二项分布的特征函数，得到了无限可整除性。然后得出了作为拉普拉斯分布和的复合负二项分布的特征函数满足连续性、二次型和无限可整除性的结论。

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The Infinite Divisibility of Compound Negative Binomial Distribution as the Sum of Laplace Distribution

The infinite divisibility of compound negative binomial distribution especially as the sum of Laplace distribution has important roles in governing the mathematical model based on its characteristic function. In order to show the property of characteristic function of this compound negative binomial distribution, it is used Fourier-Stieltjes transform to have characteristic function and then governed the property of continuity and quadratic form by using analytical approaches. The infinite divisibility property is obtained by introducing a function satisfied the criteria to be a characteristic function such that its convolution has the characteristic function of compound negative binomial distribution. Then it is concluded that the characteristic function of compound negative binomial distribution as the sum of Laplace distribution satisfies the property of continuity, quadratic form and infinite divisibility.

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来源期刊

Pakistan Journal of Statistics and Operation Research STATISTICS & PROBABILITY-

CiteScore

3.30

自引率

26.70%

发文量

期刊介绍： Pakistan Journal of Statistics and Operation Research. PJSOR is a peer-reviewed journal, published four times a year. PJSOR publishes refereed research articles and studies that describe the latest research and developments in the area of statistics, operation research and actuarial statistics.