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Count regression models are important statistical tools to model the discrete dependent variable with known covariates. When the dependent variable exhibits over-dispersion and inflation at zero point, the zero-inflated negative-binomial regression model is used. The presented paper offers a new model as an alternative to the zero-inflated negative-binomial regression model. To do this, Poisson generalized-Lindley distribution is re-parametrized and its parameter estimation problem is discussed via maximum likelihood estimation method. The proposed model is called as zero-inflated Poisson generalized Lindley regression model. The results regarding the efficiency of parameter estimation of the proposed model are evaluated with two simulation studies. To evaluate the success of the proposed model in the case of zero inflation, two datasets are analyzed. According to the results obtained, the proposed model gives better results than the negative-binomial regression model both in case of over-dispersion and in the case of zero inflation.

In this paper, a newbounded generalization of the unit-Gompertz distribution called the Marshall-Olkin extended unit-Gompertz distribution (MOEUGD) is introduced. The mathematical properties and an associated quantile regression model of the proposed distribution are derived. The maximum likelihood estimation method is employed for estimating the parameters of the proposed distribution, and a Monte Carlo simulation study is carried out to investigate the asymptotic behaviour of the parameter estimates of the proposed distribution. Finally, the applicability of the proposed distribution is illustrated by means of two real data sets defined on a unit-interval andan application of the regression model to a real data set.

This study proposes a new one-parameter discrete distribution, called a discrete Bilal distribution. The structural properties of the proposed distributions, including the shape of the probability mass function, mode, moments, skewness, kurtosis, index of dispersion, mean deviation, stress-strength reliability, and order statistics, are derived. These properties are expressed in closed-forms. The maximum likelihood and method of moments estimation methods are considered to estimate the unknown model parameter. An extensive simulation study is carried out to examine the finite sample performance of estimation methods. The usefulness of the proposed model is illustrated in the first-order integer-valued autoregressive process. The empirical importance of the proposed models is proved through three real data applications.

This paper introduces a new extension of the gamma distribution, named as a new extended gamma distribution, via mixture representation of xgamma and gamma distributions. The statistical properties of the proposed distribution are derived such as moment generating and characteristic functions, variance, skewness, and kurtosis measures, Lorenz curve, and mean residual life function. The maximum likelihood, parametric bootstrap, method of moments, least squares, and weighted least squares estimation methods are considered to obtain the unknown model parameters. The finite sample performance of estimation methods is discussed via a simulation study. Using the proposed distribution, we propose a new regression model for the right-skewed response variable as an alternative to the gamma regression model. Two real data sets are analyzed to convince the readers for the usefulness of the proposed model.

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing than simpler models. In this paper, a new mixture family of the lifetime distributions is introduced via harmonic weighted mean of an underlying distribution and the distribution of the proportional hazard model corresponding to the baseline model. The proposed class of distributions includes the general Marshall-Olkin family of distributions as a special case. Some important properties of the proposed model such as survival function, hazard function, order statistics and some results on stochastic ordering are obtained in a general setting. A special case of this new family is considered by employing Weibull distribution as the parent distribution. We derive several properties of the special distribution such as moments,hazard function survival regression and certain characterizations results. Moreover, we estimate the parameters of the model by using frequentist and Bayesian approaches. For Bayesian analysis, five loss functions, namely the squared error loss function (SELF), weighted squared error loss function (WSELF), modified squared error loss function (MSELF), precautionary loss function (PLF), and K-loss function (KLF) are considered. The beta prior as well as the gamma prior are used to obtain the Bayes estimators and posterior risk of the unknown parameters of the model. Furthermore, credible intervals (CIs) and highest posterior density (HPD) intervals are also obtained. A simulation study is presented via Monte Carlo to investigate the bias and mean square error of the maximum likelihood estimators. For illustrative purposes, two real-life applications of the proposed distribution to Kidney and cancer patients are provided.

A new one-parameter discrete distribution, namely discrete Burr-Hatke distribution is introduced and its mathematical properties are studied comprehensively. The main properties of the discrete Burr-Hatke distribution such as mean, variance, skewness and kurtosis measures are obtained in explicit forms. Several parameter estimation methods are used to obtain unknown model parameters and these estimation methods are compared via simulation study. The discrete Burr-Hatke distribution is over-dispersed since its variance is greater than its mean. This property of the proposed distribution opens a new opportunity to model over-dispersed data sets. To show the importance of the proposed distribution against the existing discrete probability distributions, three data sets in different fields are analyzed. Additionally, count regression model based on the discrete Burr-Hatke distribution is introduced with its residual analysis.

The aim of this article is to propose a new three-parameter discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, index of dispersion, mean residual life, mean past life and stress-strength reliability. These properties are expressed in explicit forms. The maximum likelihood approach is used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of the estimators. Using the proposed distribution, a new first-order integer-valued autoregressive process is introduced for the over-dispersed, equi-dispersed and under-dispersed time series of counts. To demonstrate the importance of the proposed distribution, three data sets on coronavirus, length of stay at psychiatric ward and monthly counts of larceny calls are analyzed.

A new distribution defined on (0,1) interval is introduced. Its probability density and cumulative distribution functions have simple forms. Thanks to its simple forms, the moments, incomplete moments and quantile function of the proposed distribution are derived and obtained in explicit forms. Four parameter estimation methods are used to estimate the unknown parameter of the distribution. Besides, simulation study is implemented to compare the efficiencies of these parameter estimation methods. More importantly, owing to the proposed distribution, we provide an alternative regression model for the bounded response variable. The proposed regression model is compared with the beta and unit-Lindley regression models based on two real data sets.

Lifetime distributions are an important statistical tools to model the different characteristics of lifetime data sets. The statistical literature contains very sophisticated distributions to analyze these kind of data sets. However, these distributions have many parameters which cause a problem in estimation step. To open a new opportunity in modeling these kind of data sets, we propose a new extension of half-logistic distribution by using the odd Lindley-G family of distributions. The proposed distribution has only one parameter and simple mathematical forms. The statistical properties of the proposed distributions, including complete and incomplete moments, quantile function and Rényi entropy, are studied in detail. The unknown model parameter is estimated by using the different estimation methods, namely, maximum likelihood, least square, weighted least square and Cramer-von Mises. The extensive simulation study is given to compare the finite sample performance of parameter estimation methods based on the complete and progressive Type-II censored samples. Additionally, a new log-location-scale regression model is introduced based on a new distribution. The residual analysis of a new regression model is given comprehensively. To convince the readers in favour of the proposed distribution, three real data sets are analyzed and compared with competitive models. Empirical findings show that the proposed one-parameter lifetime distribution produces better results than the other extensions of half-logistic distribution.

In this paper, a new family of distributions with one extra shape parameter, called the xgamma-G, is proposed. comprehensive treatment of some of its mathematical properties including ordinary and incomplete moments and quantile and generating functions are derived. The unknown model parameters are estimated by the maximum likelihood method and the performance of the maximum likelihood estimators are assessed via two extensive simulation studies. Additionally, the log-location-scale regression model for censored data based on a special member of the family is introduced. The usefulness of the proposed models is illustrated utilizing three real data sets.

We introduce a new flexible class of continuous distributions via the Hjorth's IDB model. We provide some mathematical properties of the new family. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. The maximum likelihood method is used for estimating the model parameters. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of the simulation study. A new regression model as well as residual analysis are presented. Finally, the usefulness of the family is illustrated by means of four real data sets. The new model provides consistently better fits than other competitive models for these data sets.

We propose a new class of continuous distributions called the generalized Kumaraswamy-G family which extends the Kumaraswamy-G family defined by Cordeiro and de Castro [1]. Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi entropy, order statistics and characterizations are derived. The new location-scale regression model is introduced based on the new generated distribution. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.

When the response variable is defined on the (0,1) interval, the beta and simplex regression models are commonly used by researchers. However, there is no software support for these models to make their implementation easy for researchers. In this study, we developed a web-tool, named SimBetaReg, to help researchers who are not familiar with programming to implement the beta and simplex regression models. The developed application is free and works independently from the operating systems. Additionally, we model the incidence ratios of COVID-19 with educational and civic engagement indicators of the OECD countries using the SimBetaReg web-tool. Empirical findings show that when the educational attainment, years in education, and voter turnout increase, the incidence ratios of the countries decrease.

Recently, bounded distributions have attracted attention. These distributions are frequently used in modeling rate and proportion data sets. In this study, a new alternative model is proposed for modeling bounded data sets. Parameter estimations of the proposed distribution are obtained via maximum likelihood method. In addition, a new regression model is defined under the proposed distribution and its residual analysis is examined. As a result of the empirical studies on real data sets, it is observed that the proposed regression model gives better results than the unit-Weibull and Kumaraswamy regression models.

This paper introduces a new family of distributions based on the additive model structure. Three submodels of the proposed family are studied in detail. Two simulation studies were performed to discuss the maximum likelihood estimators of the model parameters. The log location-scale regression model based on a new generalization of the Weibull distribution is introduced. Three datasets were used to show the importance of the proposed family. Based on the empirical results, we concluded that the proposed family is quite competitive compared to other models.

A new three parameter model called the odd log-logistic Marshall-Olkin-Lindley (OLLMO-L) distribution is proposed and studied. This distribution is symmetric, platykurtic, leptokurtic and unimodal. Various structural properties are derived, including explicit expressions for the ordinary and conditional moments, generating function and order statistics. We use maximum likelihood method to estimate the parameters of model. Simulation studies for some particular cases are also run to assess the performance of the maximum likelihood estimators. We prove empirically that the proposed distribution is a very competitive model to other classical models by means of two real data sets.