For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G, and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for the estimation of G-family parameters. We investigate the properties of one special model called the new Kumaraswamy-Weibull (NKwW) distribution. Parameters of NKwW model are estimated by using maximum likelihood method, and the performance of these estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of the proposed model. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull and exponentiated-Weibull distributions when applied to these data sets. The bivariate extension of the family is also proposed, and the estimation of parameters is dealt. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

The future values of the expected claims are very important for the insurance companies for avoiding the big losses under uncertainty which may be produced from future claims. In this paper, we define a new size-of-loss distribution for the negatively skewed insurance claims data. Four key risk indicators are defined and analyzed under four estimation methods: maximum likelihood, ordinary least squares, weighted least squares, and Anderson Darling. The insurance claims data are modeled using many competitive models and comprehensive comparison is performed under nine statistical tests. The autoregressive model is proposed to analyze the insurance claims data and estimate the future values of the expected claims. The value-at-risk estimation and the peaks-over random threshold mean-of-order-p methodology are considered.

We introduce and study general mathematical properties of a new generator of continuous distributions with one extra parameter called the generalized odd half-Cauchy family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear mixture of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the flexibility of the new family by means of two real data sets.

We introduce here a new distribution called the power-modified Kies-exponential (PMKE) distribution and derive some of its mathematical properties. Its hazard function can be bathtub-shaped, increasing, or decreasing. Its parameters are estimated by seven classical methods. Further, Bayesian estimation, under square error, general entropy, and Linex loss functions are adopted to estimate the parameters. Simulation results are provided to investigate the behavior of these estimators. The estimation methods are sorted, based on partial and overall ranks, to determine the best estimation approach for the model parameters. The proposed distribution can be used to model a real-life turbocharger dataset, as compared with 24 extensions of the exponential distribution.