In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

A new four-parameter lifetime distribution (called the Topp Leone Weibull-Lomax distribution) is proposed in this paper. Different mathematical properties of the proposed distribution were studied which include quantile function, ordinary and incomplete moments, probability weighted moment, conditional moments, order statistics, stochastic ordering, and stress-strength reliability parameter. The regression model and the residual analysis for the proposed model were also carried out. The model parameters were estimated by using the maximum likelihood criterion and the behaviour of these estimated parameters were examined by conducting a simulation study. The importance and flexibility of the proposed distribution have been proved empirically by using four separate data sets.

In this article, Burr III distribution is proposed with a significantly improved functional form. This new modification has enhanced the flexibility of the classical distribution with the ability to model all shapes of hazard rate function including increasing, decreasing, bathtub, upside-down bathtub, and nearly constant. Some of its elementary properties, such as rth moments, sth incomplete moments, moment generating function, skewness, kurtosis, mode, ith order statistics, and stochastic ordering, are presented in a clear and concise manner. The well-established technique of maximum likelihood is employed to estimate model parameters. Middle-censoring is considered as a modern general scheme of censoring. The efficacy of the proposed model is asserted through three applications consisting of complete and censored samples.

In this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to significantly increase the flexibility of the former Burr XII distribution, with respect to the density and hazard rate shapes. Also, complementary theoretical aspects are studied as shapes, asymptotes, quantiles, useful expansion, moments, skewness, kurtosis, incomplete moments, moments generating function, stochastic ordering, reliability parameter and order statistics. Then, a Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates of the modified Burr XII model parameters. Finally, three applications to real-life data sets are presented, with models comparisons. The results are favorable for the new modified Burr XII model.

We exhibit a general family of distributions named “Kumaraswamy odd Burr G family of distributions” with four additional parameters to generalize any existing baseline distribution. Some statistical properties of the family are derived, including r^th moments, m^th incomplete moments, moment generating function and entropies. The parameters of the family are estimated by the maximum likelihood (ML) method for complete sam- ples as well as censored samples. Some sub-models of the family are considered and it is noted that their density functions can be symmetric, left-skewed, right-skewed, unimodal, bimodal and their hazard rate functions can be increasing, decreasing, bathtub, upside- down bathtub and J-shaped. Simulation is carried out for one of the sub-models to check the asymptotic behavior of the ML estimates. Applications to reliability (complete and censored) data are carried out to check the usefulness of some sub-models of the family.