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Moment Generating Function, Expectation And Variance Of Ubiquitous Distributions With Applications In Decision Sciences: A Review

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  • Kim-Hung Pho

    (Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)

  • Thi Diem-Chinh Ho

    (Faculty of Mathematics and Statistics, University of Natural Sciences, Ho Chi Minh City, Vietnam)

  • Tuan-Kiet Tran

    (College of Science, Can Tho University, Viet Nam)

  • Wing-Keung Wong

    (Department of Finance, Fintech Center, and Big Data Research Center, Asia University, Taiwan)

Abstract

Statistics have been widely used in many disciplines including science, social science, business, engineering, and many others. One of the most important areas in statistics is to study the properties of distribution functions. To bridge the gap in the literature, this paper presents the theory of some important distribution functions and their moment generating functions. We introduce two approaches to derive the expectations and variances for all the distribution functions being studied in our paper and discuss the advantages and disadvantages of each approach in our paper. In addition, we display the diagrams of the probability mass function, probability density function, and cumulative distribution function for each distribution function being investigated in this paper. Furthermore, we review the applications of the theory discussed and developed in this paper to decision sciences.

Suggested Citation

  • Kim-Hung Pho & Thi Diem-Chinh Ho & Tuan-Kiet Tran & Wing-Keung Wong, 2019. "Moment Generating Function, Expectation And Variance Of Ubiquitous Distributions With Applications In Decision Sciences: A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 65-150, June.
    • Handle: RePEc:aag:wpaper:v:23:y:2019:i:2:p:65-150
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    More about this item

    Keywords

    Moment Generating Function; Expectation; Variance; Distribution Functions;
    All these keywords.

    JEL classification:

    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy
    • O34 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Intellectual Property and Intellectual Capital

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