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This research introduces a shifted Kumaraswamy distribution (SKD). The SKD is capable of modelling real-world phenomena with asymmetrical and bathtub-shaped characteristics with exceptional proficiency. The mathematical and reliability characteristics are thoroughly examined. To better comprehend its behaviour, density and hazard rate functions are plotted. The parameters of the model are estimated through the use of the maximum likelihood estimation method. The effectiveness of the SKD is demonstrated through its application to four real-world lifetime datasets, resulting in significantly improved outcomes compared to other well-known models and providing the closest fit to the data. This superiority confirms the SKD as a preferable choice over the baseline model. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new class that generates flexible optimal models. The appropriate features of the new class and a special member are studied by utilizing analytical, graphical, and numerical methodologies. For the estimation of unknown parameters, the maximum likelihood, least-square, and percentile methods are discussed and selection is based on bias and mean square error via an extensive simulation study. Five-life time data sets are evaluated, revealing that the new class has a significant advantage over well-known competitors. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new model, capable of modeling against the bathtub shaped failure rate phenomena, referred to as the Lehmann-II Muhammad (L-II-M) distribution. We derived some mathematical and reliability characteristics developed some explicit expressions for the moments, quantile function, and order statistics. We suggested a method of maximum likelihood estimator for the estimation of model parameters, and a simulation study was recommended to observe the asymptotic behavior of MLEs. The strength of L-II-M distribution was affirmed by modeling in two suitable lifetime engineering datasets. [ABSTRACT FROM AUTHOR]