Marshall and Olkin (1997) proposed a new method to establish more flexible new families of distributions by adding a parameter to a distribution. In this article, Marshall-Olkin extended Burr type XII (MOEBXII) distribution is introduced. Properties of MOEBXII distribution are studied and analyzed. Based on complete sample, maximum likelihood and Bayesian estimators of the parameters are derived. Application to a real data set is carried out to illustrate the flexibility of the model.

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.

The beta generalized inverse Weibull distribution (BGIW) is suggested in this paper. The mathematical properties of the BGIW distribution are provided and the expression for the moment generating function is derived. Also, the analytical shapes of the corresponding probability density function, reliability function, hazard rate function, and mode are derived with graphical illustrations. Expressions for the r-th positive and negative moments are calculated and the variation of the skewness and kurtosis measures is investigated. Moment and likelihood estimators of the parameters are derived. The observed information matrix is obtained. Simulation study is carried out to investigate the performance of the maximum likelihood method of estimation. Moreover, analysis of real data set is conducted to demonstrate the usefulness of the proposed distribution.

In the process of identifying potential anticancer agents, the ability of a new agent is tested for cytotoxic activity against a panel of standard cancer cell lines. The National Cancer Institute (NCI) present the cytotoxic profile for each agent as a set of estimates of the dose required to inhibit the growth of each cell line. The NCI estimates are obtained from a linear interpolation method applied to the dose-response curves. In this paper non-linear fits are proposed as an alternative to interpolation. This is illustrated with data from two agents recently submitted to NCI for potential anticancer activity. Fitting of individual non-linear curves proved difficult, but a non-linear mixed model applied to the full set of cell lines overcame most of the problems. Two non-linear functional forms were fitted using random effect models by both maximum likelihood and a full Bayesian approach. Model-based toxicity estimates have some advantages over those obtained from interpolation. They provide standard errors for toxicity estimates and other derived quantities, allow model comparisons. Examples of each are illustrated.

This study introduces a new extended distribution of the Burr Type X distribution, using Marshall-Olkin method called the Marshall-Olkin Extended Burr Type X distribution. This study formulates the new distribution by inducing a tilt parameter in the Burr Type X distribution of Marshall-Olkin, to account for the significance of the size of an event. Model parameters are obtained using maximum likelihood and Bayesian methods of estimation. The scale and shape parameters are specifically defined to identify the dimensions and density of an event. Mathematical and statistical properties and limitations of the distribution are also presented. Lifetime data analysis is performed to demonstrate the model's applicability and flexibility. Akaike and Bayesian Information Criteria illustrate that the new distribution provides better fit compared to other distributions,