Bounded risk per unit cost index constraint for sequential estimation of the mean in a two-parameter exponential distribution

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
E. Mahmoudi, Zahra Nemati, Ashkan Khalifeh
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引用次数: 1

Abstract

Abstract In this article, the two-stage sequential sampling procedure is proposed to estimate the mean of an exponential distribution under the modified square error loss function. The main aim of the article is to consider the associated risk per unit cost function by bounding it from above with a fixed preassigned positive number, ω. We provide the exact distribution of the total sample size, explicit formulas for the mathematical expectation of the rth power of the total sample size, the expected value and mean squared error of the maximum likelihood estimate of the scale, and mean parameters of the exponential distribution under the two-stage sequential procedure. The performances of the proposed methodologies are investigated with the help of simulations. In the end, we supplement with extensive sets of data analysis via computer simulations, validating that the two-stage sequential method performs very well. Finally, using a real data set, the procedure is clearly illustrated.
双参数指数分布均值序列估计的单位成本指数有界风险约束
摘要本文提出了在修正的平方误差损失函数下估计指数分布均值的两阶段序列抽样方法。本文的主要目的是通过将单位成本函数与固定的预先分配的正数ω从上面进行绑定来考虑相关的风险。我们给出了总样本量的精确分布,总样本量四次方的数学期望的显式公式,标度最大似然估计的期望值和均方误差,以及两阶段序列过程下指数分布的平均参数。在仿真的帮助下,对所提出的方法的性能进行了研究。最后,我们通过计算机模拟补充了大量的数据分析,验证了两阶段序列方法的性能。最后,使用真实的数据集,清楚地说明了该过程。
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
CiteScore
1.40
自引率
12.50%
发文量
20
期刊介绍: The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.
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