期刊名称：Journal of Statistical Theory and Applications (JSTA)
电子版ISSN：1538-7887
出版年度：2020
卷号：19
期号：2
页码：173-184
DOI：10.2991/jsta.d.200513.001
语种：English
出版社：Atlantis Press
摘要：In certain experimental investigations involving discrete distributions external factors may induce measurement error in the form of misclassification. For instance, a situation may arise where certain values are erroneously reported; such a situation termed as modified or misclassified has been studied by many researchers. Cohen (J. Am. Stat. Assoc. 55 (1960), 139–143; Ann. Inst. Stat. Math. 9 (1960), 189–193; Technometrics. 2 (1960), 109–113) studied misclassification in Poisson and the binomial random variables. In this paper, we discuss misclassification in the most general class of discrete distributions, the generalized power series distributions (GPSDs), where some of the observations corresponding to x=c+1; c≥0 are erroneously observed or at least reported as being x=c with probability α. This class includes among others the binomial, negative binomial, logarithmic series and Poisson distributions. We derive the Bayes estimators of functions of parameters of the misclassified GPSD under different loss functions. The results obtained for misclassified GPSD are then applied to its particular cases like negative binomial, logarithmic series and Poisson distributions. Finally, few numerical examples are provided to illustrate the results.
关键词：Posterior distributions; Squared error loss function (SELF); Weighted squared error loss function (WSELF); Bayes estimators; Misclassified distributions; Negative binomial distribution; Logarithmic series distribution; Poisson distribution
