Misclassified size-biased modified power series distribution and its applications

Hassan, Anwar; Ahmad, Peer Bilal

doi:10.21136/mb.2009.140633

Cited by 3 publications

(1 citation statement)

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“…Jani and Shah [10] studied misclassification in modified power series distributions (MPSDs) and Patel and Patel [11] in case of generalized power series distribution (GPSD), where some of the values of one are sometimes reported as zero. Hassan and Ahmad [12] studied misclassification in size-biased modified power series distributions (SBMPSDs), where some of the observations corresponding to x = 2 are misclassified as x = 1. Patel and Patel [13] also studied misclassification in MPSD and Hassan and Ahmad [14] in SBMPSD for a more general situation where sometimes the value (c + 1) is reported erroneously to c. In all these five papers the authors studied the structural properties of the respective distributions.…”

Section: Introductionmentioning

confidence: 99%

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

Ahmad¹

2020

JSTA

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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.

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Section: Introductionmentioning

confidence: 99%

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

Ahmad¹

2020

JSTA

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On the Bayes estimators of the parameters of size-biased generalized power series distributions

Ahmad

2015

Communications in Statistics - Theory and Methods

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Estimation in Misclassified Size-Biased Generalized Negative Binomial Distribution

Trivedi¹,

Patel²

2013

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Misclassified size-biased modified power series distribution and its applications

Cited by 3 publications

References 3 publications

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

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

On the Bayes estimators of the parameters of size-biased generalized power series distributions

Estimation in Misclassified Size-Biased Generalized Negative Binomial Distribution

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