Estimation of P(X ≤ Y) for discrete distributions with non-identical support

Q4 Mathematics

Statistics in Transition Pub Date : 2022-09-01 DOI:10.2478/stattrans-2022-0029

M. Choudhury, Rahul Bhattacharya, Sudhansu S. Maiti

引用次数: 0

Abstract

Abstract The Uniformly Minimum Variance Unbiased (UMVU) and the Maximum Likelihood (ML) estimations of R = P(X ≤ Y) and the associated variance are considered for independent discrete random variables X and Y. Assuming a discrete uniform distribution for X and the distribution of Y as a member of the discrete one parameter exponential family of distributions, theoretical expressions of such quantities are derived. Similar expressions are obtained when X and Y interchange their roles and both variables are from the discrete uniform distribution. A simulation study is carried out to compare the estimators numerically. A real application based on demand-supply system data is provided.

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具有非完全支持的离散分布的P（X≤Y）的估计

摘要对独立的离散随机变量X和Y，考虑了R = P(X≤Y)及其相关方差的一致最小方差无偏估计(UMVU)和最大似然估计(ML)，假设X的分布是离散的均匀分布，Y的分布是离散的单参数指数分布族的成员，导出了这两个量的理论表达式。当X和Y互换角色，且两个变量均为离散均匀分布时，得到类似的表达式。通过仿真研究，对两种估计方法进行了数值比较。给出了基于供需系统数据的实际应用。

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

Statistics in Transition Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

9 weeks

期刊介绍： Statistics in Transition (SiT) is an international journal published jointly by the Polish Statistical Association (PTS) and the Central Statistical Office of Poland (CSO/GUS), which sponsors this publication. Launched in 1993, it was issued twice a year until 2006; since then it appears - under a slightly changed title, Statistics in Transition new series - three times a year; and after 2013 as a regular quarterly journal." The journal provides a forum for exchange of ideas and experience amongst members of international community of statisticians, data producers and users, including researchers, teachers, policy makers and the general public. Its initially dominating focus on statistical issues pertinent to transition from centrally planned to a market-oriented economy has gradually been extended to embracing statistical problems related to development and modernization of the system of public (official) statistics, in general.