A unified exponential-H family for modeling real-life data: Properties and inference.

The exponential distribution is one of the most widely used statistical distribution for reliability issues. In this paper, we introduce a novel family based on the exponential model, called the new exponential-H (NEx-H) family. The sub-models of the NEx-H family are capable of accommodating variable failure rates, as well as unimodal, bimodal, left-skewed, symmetric, right-skewed, and J-shape densities. The mathematical features of the NEx-H family are derived. The parameters of the NEx-Weibull distribution are estimated by using seven estimation methods. Detailed numerical simulations are presented. Based on our study, the maximum likelihood is the best estimation method for estimating the NEx-Weibull parameters. Three real-life data sets are fitted using the NEx-Weibull distribution. The NEx-Weibull model provides better fit as compared to some competing Weibull models.

New generalized class of estimators for estimation of finite population mean based on probability proportional to size sampling using two auxiliary variables: A simulation study.

This article aims to suggest a new generalized class of estimators based on probability proportional to size sampling using two auxiliary variables. The numerical expressions for the bias and mean squared error (MSE) are derived up to the first order of approximation. Four actual data sets are used to examine the performances of a new improved generalized class of estimators. From the results of real data sets, it is examined that the suggested estimator gives the minimum MSE and the percentage relative efficiency is higher than all existing estimators, which shows the importance of the new generalized class of estimators. To check the strength and generalizability of our proposed class of estimators, a simulation study is also accompanied. The consequence of the simulation study shows the worth of newly found proposed class estimators. Overall, we get to the conclusion that the proposed estimator outperforms as compared to all other estimators taken into account in this study.

Copula-based Markov zero-inflated count time series models with application.

Count time series data with excess zeros are observed in several applied disciplines. When these zero-inflated counts are sequentially recorded, they might result in serial dependence. Ignoring the zero-inflation and the serial dependence might produce inaccurate results. In this paper, Markov zero-inflated count time series models based on a joint distribution on consecutive observations are proposed. The joint distribution function of the consecutive observations is constructed through copula functions. First- and second-order Markov chains are considered with the univariate margins of zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), or zero-inflated Conway-Maxwell-Poisson (ZICMP) distributions. Under the Markov models, bivariate copula functions such as the bivariate Gaussian, Frank, and Gumbel are chosen to construct a bivariate distribution of two consecutive observations. Moreover, the trivariate Gaussian and max-infinitely divisible copula functions are considered to build the joint distribution of three consecutive observations. Likelihood-based inference is performed and asymptotic properties are studied. To evaluate the estimation method and the asymptotic results, simulated examples are studied. The proposed class of models are applied to sandstorm counts example. The results suggest that the proposed models have some advantages over some of the models in the literature for modeling zero-inflated count time series data.