In this paper, we introduce a new generalization of Aradhana distribution called as Weighted Aradhana Distribution (WID). The statistical properties of this distribution are derived and the model parameters are estimated by maximum likelihood estimation. Simulation study of ML estimates of the parameters is carried out in R software. Finally, an application to real data set is presented to examine the significance of newly introduced model.

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The values of the expected frequencies clearly shows that the zero-inflated Poisson distribution provided a closer fit than that provided by the classical Poisson distribution. It is also clear from the table that the Bayes estimators obtained under weighted squared error loss functions (WSELF) gives closer fits than the Bayes estimator obtained under squared error loss function (SELF). Also, the exponentially minimum expected loss (EWMEL) estimates gives better fits than the minimum expected loss (MEL) estimates. Keeping in view the importance of count data modeling it is recommended that whenever the experimental number of zeros are more than that given by the model, the model should be adjusted accordingly to account for the extra zeros.

By starting from the one-parameter Modified Borel-Tanner distribution proposed recently in the statistic literature, we introduce the zero-inflated Modified Borel-Tanner distribution. Additionally, on the basis of the proposed zero-inflated distribution, a novel zero-inflated regression model is proposed, which is quite simple and may be an interesting alternative to usual zero-inflated regression models for count data. The parameters of the proposed model are estimated by Maximum Likelihood Estimation technique. To check the potentiality of the zero inflated Modified Borel-Tanner regression, an application to the count of infected blood cells is taken. The results suggest that the new zero inflated Modified Borel-Tanner regression is more appropriate to model these count data than other familiar zero-inflated (or not) regression models commonly used in practice.

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.