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Misclassification in Size-Biased Modified Power Series Distribution and Its Applications
Anwar Hassan,Peer Bilal Ahmad 한국산업응용수학회(구 한국산업정보응용수학회) 2009 한국산업정보응용수학회 Vol.13 No.1
A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x=c+1 are misclassified as x = c with probability α, is defined. We obtain its recurrence relations among the raw moments, the central moments and the factorial moments. Discussion of the effect of the misclassification on the variance is considered. To illustrate the situation under consideration some of its particular cases like the size-biased generalized negative binomial (SBGNB), the size-biased generalized Poisson (SBGP) and size-biased Borel distributions are included. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results.
( Anwar Hassan ),( Peer Bilal Ahmad ),( M. Ishaq Bhatti ) 한국산업응용수학회(구 한국산업정보응용수학회) 2008 한국산업정보응용수학회 Vol.12 No.2
In this paper Bayes estimator of the parameter and reliability function of the zero-truncated Poisson distribution are obtained. Furthermore, recurrence relations for the estimator of the parameter are also derived. Monte Carlo simulation technique has been made for comparing the Bayes estimator and reliability function with the corresponding maximum likelihood estimator (MLE) of zero-truncated Poisson distribution.
ANWAR HASSAN,PEER BILAL AHMAD,M. ISHAQ BHATTI 한국산업응용수학회 2008 Journal of the Korean Society for Industrial and A Vol.12 No.2
In this paper Bayes estimator of the parameter and reliability function of the zero-truncated Poisson distribution are obtained. Furthermore, recurrence relations for the estimator of the parameter are also derived. Monte Carlo simulation technique has been made for comparing the Bayes estimator and reliability function with the corresponding maximum likelihood estimator (MLE) of zero-truncated Poisson distribution.
MISCLASSIFICATION IN SIZE-BIASED MODIFIED POWER SERIES DISTRIBUTION AND ITS APPLICATIONS
ANWAR HASSAN,PEER BILAL AHMAD 한국산업응용수학회 2009 Journal of the Korean Society for Industrial and A Vol.13 No.1
A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x = c + 1 are misclassified as x = c with probability α, is defined. We obtain its recurrence relations among the raw moments, the central moments and the factorial moments. Discussion of the effect of the misclassification on the variance is considered. To illustrate the situation under consideration some of its particular cases like the size-biased generalized negative binomial (SBGNB), the size-biased generalized Poisson (SBGP) and sizebiased Borel distributions are included. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results.
Zero-inflated Poisson-Akash distribution for count data with excessive zeros
Wani Mohammad Kafeel,Ahmad Peer Bilal 한국통계학회 2023 Journal of the Korean Statistical Society Vol.52 No.3
Over-dispersed models are often used whenever the variation is more than what in point of fact is anticipated by a model. One of the reasons behind experiencing over-dispersion is an excessive number of zeros, hence when modeling this observed fact, we use zero-inflated models rather than more traditional ones. As a part of our research, we have suggested a zero-inflated variant of Poisson-Akash distribution that was introduced in 2015. We have calculated crucial statistical characteristics of the suggested model which are not confined to generating functions, over-dispersion property, moments and associated measures. The parametric estimation has been carried out using the maximum likelihood estimation. Two different simulation exercises have been carried out, one to test the performance of maximum likelihood estimates and the other for testing the compatibility of our devised model when data has been simulated from different zero-inflated models. For the purpose of testing the compatibility of our proposed model, we have used four real life data sets and considered different performance measures like Goodness-of-fit, Akaike’s information criterion, Bayesian information criterion, Dispersion index etc. The fitting results have been compared with some other models of interest. Moreover, we have tested the significance of the zero-inflation parameter using Likelihood ratio test, Score test and the Wald test itself.