Bayesian Analysis of Misclassified Generalized Power Series Distributions Under Different Loss Functions

DOI

10.2991/jsta.d.200513.001How to use a DOI?

Keywords

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

Abstract

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.

Copyright

© 2020 The Authors. Published by Atlantis Press SARL.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Peer Bilal Ahmad
PY  - 2020
DA  - 2020/05/25
TI  - Bayesian Analysis of Misclassified Generalized Power Series Distributions Under Different Loss Functions
JO  - Journal of Statistical Theory and Applications
SP  - 173
EP  - 184
VL  - 19
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.200513.001
DO  - 10.2991/jsta.d.200513.001
ID  - Ahmad2020
ER  -