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In this paper, we develop a mixture of autoregressive (MoAR) process model with time varying and freely indexed covariates under the flexible class of two–piece distributions using the scale mixtures of normal (TP-SMN) family. This novel family of time series (TP-SMN-MoAR) models was used to examine flexible and robust clustering of reported cases of Covid-19 across 313 counties in the U.S. The TP-SMN distributions allow for symmetrical/ asymmetrical distributions as well as heavy-tailed distributions providing for flexibility to handle outliers and complex data. Developing a suitable hierarchical representation of the TP-SMN family enabled the construction of a pseudo-likelihood function to derive the maximum pseudo-likelihood estimates via an EM-type algorithm. [ABSTRACT FROM AUTHOR]

Multi-collinearity among regressors and consequently ill-conditioning inflates the mean squared error (MSE) of the maximum likelihood estimator (MLE) of the parameters in a regression model. In recent years, the Liu estimator (LE) has been widely used in the literature to improve the regression models. Since in some regression models, the dependent variable follows a double bounded distribution, such as the beta and Kumaraswamy distributions, we are going to consider these two regression models in the presence of a multi-collinearity problem with investigation of their properties, characterizations, MLEs, and LEs. Finally, MSEs of LEs and MLEs are compared under various link functions, using simulation and two real data sets. [ABSTRACT FROM AUTHOR]

In this paper, a new bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distributions, is studied. It is observed that the proposed bivariate distribution is a flexible distribution whose cumulative distribution function has an analytical structure. In addition, a new bivariate geometric distribution can be obtained as a special case. We study different properties of this distribution and propose estimation of its parameters. We will see that the maximum of the variables involved in the proposed bivariate distribution defines some new classes of univariate discrete distributions, which are interesting in their own sake, and can be used to analyze some Reliability systems whose components are positive dependent. Some important futures of this new univariate family of discrete distributions are also studied in details. In addition, a general class of bivariate discrete distributions, whose marginals are exponentiated discrete distributions, is introduced. Moreover, the analysis of two real bivariate data sets is performed to indicate the effectiveness of the proposed models. Finally, we conclude the paper. [ABSTRACT FROM AUTHOR]

In this paper, the researchers attempt to introduce a new generalization of the Weibull-geometric distribution. The failure rate function of the new model is found to be increasing, decreasing, upside-down bathtub, and bathtub-shaped. The researchers obtained the new model by compounding Weibull distribution and discrete generalized exponential distribution of a second type, which is a generalization of the geometric distribution. The new introduced model contains some previously known lifetime distributions as well as a new one. Some basic distributional properties and moments of the new model are discussed. Estimation of the parameters is illustrated and the model with two known real data sets is examined. [ABSTRACT FROM PUBLISHER]

In this paper, a discrete analog of the beta-Weibull distribution is studied. This new distribution contams several discrete distributions ds special sub-models. Sbme distriautional and moment properties of the discrete beta-Weibull distribution as well as its order statistics are discussed. We will show that the hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and the model with a real data set is also examined. [ABSTRACT FROM AUTHOR]

A new three-parameter distribution with decreasing, increasing, bathtub-shaped and upside-down bathtub-shaped hazard rate function is proposed. The new distribution encompasses some previously known distributions as special cases. Basic mathematical properties of the new distribution (including the moment-generating function, moments, order statistics properties, Rényi entropy and stress–strength parameter) are derived. Its parameters are estimated by the method of maximum likelihood. An application is illustrated using a real data set. [ABSTRACT FROM AUTHOR]