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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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.

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This research study aims to conduct a comparative performance analysis of different scaling equations and non-scaling models used for modeling asphaltene precipitation. The experimental data used to carry out this study are taken from the published literature. Five scaling equations which include Rassamadana et al., Rassamdana and Sahimi, Hu and Gou, Ashoori et al., and log–log scaling equations were used and applied in two ways, i.e., on full dataset and partial datasets. Partial datasets are developed by splitting the full dataset in terms of Dilution ratio (R) between oil and precipitant. It was found that all scaling equations predict asphaltene weight percentage with reasonable accuracy (except Ashoori et al. scaling equation for full dataset) and their performance is further enhanced when applied on partial datasets. For the prediction of Critical dilution ratio (Rc) for different precipitants to detect asphaltene precipitation onset point, all scaling equations (except Ashoori et scaling equation when applied on partial datasets) are either unable to predict or produce results with significant error. Finally, results of scaling equations are compared with non-scaling model predictions which include PC-Saft, Flory–Huggins, and solid models. It was found that all scaling equations (except Ashoori et al. scaling equation for full dataset) either yield almost the same or improved results for asphaltene weight percentage when compared to best case (PC-Saft). However, for the prediction of Rc, Ashoori et al. scaling equation predicts more accurate results as compared to other non-scaling models.