Distributions of the Ratio and Product of Two Independent Weibull and Lindley Random Variables

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2020-05-01 DOI:10.1155/2020/5693129

N. J. Hassan, A. Nasar, J. M. Hadad

引用次数: 1

Abstract

In this paper, we derive the cumulative distribution functions (CDF) and probability density functions (PDF) of the ratio and product of two independent Weibull and Lindley random variables. The moment generating functions (MGF) and the k -moment are driven from the ratio and product cases. In these derivations, we use some special functions, for instance, generalized hypergeometric functions, confluent hypergeometric functions, and the parabolic cylinder functions. Finally, we draw the PDF and CDF in many values of the parameters.

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两个独立Weibull和Lindley随机变量的比值和乘积的分布

本文推导了两个独立威布尔和林德利随机变量的比值和乘积的累积分布函数（CDF）和概率密度函数（PDF）。矩母函数（MGF）和k矩是由比值和乘积情况驱动的。在这些推导中，我们使用了一些特殊的函数，例如广义超几何函数、合流超几何函数和抛物柱面函数。最后，我们绘制了PDF和CDF中许多值的参数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.