A new five-parameter model called the modified beta Weibull probability distribution is being introduced in this paper. This model turns out to be quite flexible for analyzing positive data and has bathtub and upside down bathtub hazard rate function. Our main objectives are to obtain representations of certain statistical functions and to estimate the parameters of the proposed distribution. As an application, the probability density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as reliability theory, hydrology, medicine, meteorology, survival analysis and engineering.
Significant progress has been made towards the generalization of some well-known lifetime models, which have been successfully applied to problems arising in several areas of research. In this paper, some properties of the new Kumaraswamy exponential-Weibull (KwEW) distribution are provided. This distribution generalizes a number of well-known special lifetime models such as the Weibull, exponential, Rayleigh, modified Rayleigh, modified exponential and exponentiated Weibull distributions, among others. The beauty and importance of the new distribution lies in its ability to model monotone and nonmonotone failure rate functions, which are quite common in environmental studies. We derive some basic properties of the KwEW distribution including ordinary and incomplete moments, skewness, kurtosis, quantile and generating functions, mean deviations and Shannon entropy. The method of maximum likelihood and a Bayesian procedure are used for estimating the model parameters. By means of a real lifetime data set, we prove that the new distribution provides a better fit than the Kumaraswamy Weibull, Marshall-Olkin exponential-Weibull, extended Weibull, exponential-Weibull and Weibull models. The application indicates that the proposed model can give better fits than other well-known lifetime distributions.
Development and application of probability models in data analysis are of major importance for all sciences. Therefore, we introduce a new model called a power log-Dagum distribution defined on the entire real line. The model contains many new sub-models: power logistic, linear log-Dagum, linear logistic and log-Dagum distributions among them. Some properties of the model including three different estimation procedures are justified. The model exhibits various shapes for the density and hazard rate functions. Moreover, the estimation procedures are compared using simulation studies. Finally, the model with others are fitted to three data sets and it shows a better fit than the compared distributions defined on the real line.
In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modified Weibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.
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