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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]