In this paper, we define a new extension of Srivastava’s triple
hypergeometric functions by using a new extension of Pochhammer’s symbol that was recently proposed by Srivastava, Rahman and Nisar [H. M. Srivastava, G. Rahman and K. S. Nisar,
Some extensions of the Pochhammer symbol and the associated hypergeometric functions,
Iran. J. Sci. Technol. Trans. A Sci. 43 2019, 5, 2601–2606]. We present their certain basic
properties such as integral representations, derivative formulas, and
recurrence relations. Also, certain new special cases have been identified
and some known results are recovered from main results.
We introduce and study the Marshall-Olkin additive Weibull distribution in order to allow a wide variation in the shape of the hazard rate, including increasing, decreasing, bathtub and unimodal shapes. The new distribution generalizes at least eleven lifetime models extant in the literature. Various of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, moments of the residual and reversed residual life functions and order statistics are derived. The parameters of the new distribution are estimated by the maximum likelihood method. We illustrate empirically the superiority of the new model over other distributions by means of a real life data set.
A generalization of the exponentiated Weibull geometric model called the transmuted exponentiated Weibull geometric distribution is proposed and studied. It includes as special cases at least ten models. Some of its structural properties including order statistics, explicit expressions for the ordinary and incomplete moments and generating function are derived. The estimation of the model parameters is performed by the maximum likelihood method. The use of the new lifetime distribution is illustrated with an example. We hope that the proposed distribution will serve as a good alternative to other models available in the literature for modeling positive real data in several areas.
A new four-parameter model called the Marshall-Olkin exponential-Weibull probability distribution is being introduced in this paper, generalizing a number of known lifetime distributions. This model turns out to be quite flexible for analyzing positive data. The hazard rate functions of new model can be increasing and bathtub shaped. Our main objectives are to obtain representations of certain associated statistical functions, to estimate the parameters of the proposed distribution and to discuss its modality. 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 as measured by the Anderson-Darling and Cramér-von Mises goodnessof-fit statistics. 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.
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