Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion, which typically occurs in count datasets. It is highly desirable to have a unified model that can automatically adapt to the underlying dispersion and that can be easily implemented in practice. In this paper, a discrete Weibull regression model is shown to be able to adapt in a simple way to different types of dispersions relative to Poisson regression: overdispersion, underdispersion and covariate-specific dispersion. Maximum likelihood can be used for efficient parameter estimation. The description of the model, parameter inference and model diagnostics is accompanied by simulated and real data analyses.

A new member of the Weibull-generated (Weibull-G) family of distributions—namely the Weibull-gamma distribution—is proposed. This four-parameter distribution can provide great flexibility in modeling different data distribution shapes. Some special cases of the Weibull-gamma distribution are considered. Several properties of the new distribution are studied. The maximum likelihood method is applied to obtain an estimation of the parameters of the Weibull-gamma distribution. The usefulness of the proposed distribution is examined by means of five applications to real datasets.

One of the most important applications of statistical analysis is in health research and applications. Cancer studies are mostly required special statistical considerations in order to find the appropriate model for fitting the survival data. Existing classical distributions rarely fit such data well and an increasing interest has been shown recently in developing more flexible distributions by introducing some additional parameters to the basic model. In this paper, a new five-parameters distribution referred as alpha power Kumaraswamy Weibull distribution is introduced and studied. Particularly, this distribution extends the Weibull distribution based on a novel technique that combines two well known generalisation methods, namely, alpha power and T-X transformations. Different characteristics of the proposed distribution, including moments, quantiles, Rényi entropy and order statistics are obtained. The method of maximum likelihood is applied in order to estimate the model parameters based on complete and censored data. The performance of these estimators are examined via conducting some simulation studies. The potential importance and applicability of the proposed distribution is illustrated empirically by means of six datasets that describe the survival of some cancer patients. The results of the analysis indicated to the promising performance of the alpha power Kumaraswamy Weibull distribution in practice comparing to some other competing distributions.

Data analysis in real life often relies mainly on statistical probability distributions. However, data arising from different fields such as environmental, financial, biomedical sciences and other areas may not fit the classical distributions. Therefore, the need arises for developing new distributions that would capture high degree of skewness and kurtosis and enhance the goodness-of-fit in empirical distribution. In this paper, we introduce a novel family of distributions which can extend some popular classes of distributions to include different new versions of the baseline distributions. The proposed family of distributions is referred as the Marshall-Olkin Weibull generated family. The proposed family of distributions is a combination of Marshall-Olkin transformation and the Weibull generated family. Two special members of the proposed family are investigated. A variety of shapes for the densities and hazard rate are presented of the considered sub-models. Some of the main mathematical properties of this family are derived. The estimation for the parameters is obtained via the maximum likelihood method. Moreover, the performance of the estimators for the considered members is examined through simulation studies in terms of bias and root mean square error. Besides, based on the new generated family, the log Marshall-Olkin Weibull-Weibull regression model for censored data is proposed. Finally, COVID-19 data and three lifetime data sets are used to demonstrate the importance of the newly proposed family. Through such an applications, it is shown that this family of distributions provides a better fit when compared with other competitive distributions.

In the following article, a new five-parameter distribution, the alpha power exponentiated Weibull-exponential distribution is proposed, based on a newly developed technique. It is of particular interest because the density of this distribution can take various symmetric and asymmetric possible shapes. Moreover, its related hazard function is tractable and showing a great diversity of asymmetrical shaped, including increasing, decreasing, near symmetrical, increasing-decreasing-increasing, increasing-constant-increasing, J-shaped, and reversed J-shaped. Some properties relating to the proposed distribution are provided. The inferential method of maximum likelihood is employed, in order to estimate the model’s unknown parameters, and these estimates are evaluated based on various simulation studies. Moreover, the usefulness of the model is investigated through its application to three real data sets. The results show that the proposed distribution can, in fact, better fit the data, when compared to other competing distributions.