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In this paper, a new two-parameter discrete logistic exponential distribution is proposed based on the survival discretization approach. Some statistical properties are derived, and it is found that the proposed model can be used to discuss several kinds of failure rates including unimodal, bathtub, and increasing-shaped. Moreover, it can be utilized effectively to model under- and over-dispersed data. The distribution parameters are estimated using the maximum likelihood technique. The behavior of maximum likelihood estimators is assessed utilizing a comprehensive simulation study. In the end, two real data are analyzed to show the usefulness of the new discrete distribution. [ABSTRACT FROM AUTHOR]

This paper deals with the statistical inference of the unknown parameters of three-parameter exponentiated power Lindley distribution under adaptive progressive type-II censored samples. The maximum likelihood estimator (MLE) cannot be expressed explicitly, hence approximate MLEs are conducted using the Newton–Raphson method. Bayesian estimation is studied and the Markov Chain Monte Carlo method is used for computing the Bayes estimation. For Bayesian estimation, we consider two loss functions, namely: squared error and linear exponential (LINEX) loss functions, furthermore, we perform asymptotic confidence intervals and the credible intervals for the unknown parameters. A comparison between Bayes estimation and the MLE is observed using simulation analysis and we perform an optimally criterion for some suggested censoring schemes by minimizing bias and mean square error for the point estimation of the parameters. Finally, a real data example is used for the illustration of the goodness of fit for this model. [ABSTRACT FROM AUTHOR]

In the statistical literature, several discrete distributions have been developed so far. However, in this progressive technological era, the data generated from different fields is getting complicated day by day, making it difficult to analyze this real data through the various discrete distributions available in the existing literature. In this context, we have proposed a new flexible family of discrete models named discrete odd Weibull-G (DOW-G) family. Its several impressive distributional characteristics are derived. A key feature of the proposed family is its failure rate function that can take a variety of shapes for distinct values of the unknown parameters, like decreasing, increasing, constant, J-, and bathtub-shaped. Furthermore, the presented family not only adequately captures the skewed and symmetric data sets, but it can also provide a better fit to equi-, over-, under-dispersed data. After producing the general class, two particular distributions of the DOW-G family are extensively studied. The parameters estimation of the proposed family, are explored by the method of maximum likelihood and Bayesian approach. A compact Monte Carlo simulation study is performed to assess the behavior of the estimation methods. Finally, we have explained the usefulness of the proposed family by using two different real data sets. [ABSTRACT FROM AUTHOR]

In the literature of distribution theory, a vast proportion is acquired by discrete distributions and their applications in real-world phenomena. However, in a rapidly changing technological era, the data generated is becoming increasingly complex day by day, making it difficult for us to capture various aspects of this real data through existing discrete models. In view of this, we propose a new flexible discrete distribution with one parameter. Some statistical and reliability are derived. These properties can be expressed as closed-forms. One of the important virtues of this newly evolved model is that it can model not only over-dispersed, positively skewed and leptokurtic data sets, but it can also be utilized for modeling increasing, decreasing and unimodal failure rate. Various estimation approaches are utilized to estimate the model parameter. A simulation study is carried out to examine the performance of the estimators for different sample size. The flexibility of the new model for analyzing different types of data is explained by utilizing four real data sets in different fields. Finally, the proposed model can serve as an alternative model to other distributions in the existing literature for modeling positive real data in several areas. [ABSTRACT FROM AUTHOR]

In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and Lmoment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences. [ABSTRACT FROM AUTHOR]

In this article, an extension of the transmuted-G family is proposed, in the so-called Poison transmuted-G family of distributions. Some of its statistical properties including quantile function, moment generating function, order statistics, probability weighted moment, stress-strength reliability, residual lifetime, reversed residual lifetime, Rényi entropy and mean deviation are derived. A few important special models of the proposed family are listed. Stochastic characterizations of the proposed family based on truncated moments, hazard function and reverse hazard function, are also studied. The family parameters are estimated via the maximum likelihood approach. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators. The advantage of the proposed family in data fitting is illustrated by means of two applications to failure time data sets. [ABSTRACT FROM AUTHOR]

This paper introduces a new univariate fl exible generator of distributions called the odd Chen-G family, and some of its statistical properties are derived. Two special models of the proposed generator are provided. The model parameters are estimated using six estimation methods, namely, maximum likelihood estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, Cramér-von Mises estimators and percentile based estimators. Further, simulations are performed to compare their performances for both small and large samples. Finally, two real datasets are used to illustrate the fl exibility of the special models of the proposed family. [ABSTRACT FROM AUTHOR]

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions. [ABSTRACT FROM AUTHOR]

Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions. [ABSTRACT FROM AUTHOR]