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This work addresses the weighted inverse Ailamujia distribution, which is an expansion of the inverse Ailamujia distribution (WIAD). Several distributional characteristics of the established distribution have been deduced and evaluated. The explicit expression of distinct ageing factors has been achieved. Several plots depict the behaviour of the probability density function (PDF) and the cumulative distribution function (CDF). The parameters of the formed distribution were estimated using the wellknown maximum likelihood methodology. Furthermore, the likelihood ratio test of the stated distribution was achieved. Eventually, two examples are offered to exemplify the effectiveness of the formulated model. [ABSTRACT FROM AUTHOR]

The family of distributions which are derived from baseline distributions drag the attention of researchers from past recent years. In this paper we introduce an extension of Gumbel type-II by using transmutation approach suggested by Shaw and Buckley (2007). Several distributional properties of the explored distribution, such as moments, moment generating function, quantile function, reliability analysis, order statistics, and Renyi entropy, have been discussed. Various diagrams depict the behaviour of the probability density function (pdf) and cumulative distribution function (cdf). The parameters of the explored distribution are calculated by using the well-known maximum likelihood procedure. Eventually, the utility of the explored distribution is shown using real life data sets. [ABSTRACT FROM AUTHOR]

Over numerous decades, academics have been attempting to develop a number of novel distributions to satisfy certain realistic demands. The rationale is that conventional distributions have generally been shown to lack fit in actual applications, such as medicinal research, engineering, hydrology, environmental science, and many more. Combining the Weibull and inverse Nadarajah Haghighi distributions generates a novel life-time distribution with four parameters, which is referred to as the Weibull-inverse Nadarajah Haghighi (WINH) distribution. Different structural characteristics of the formulated distribution have been determined and analysed. Distinct plots depict the behaviour of the probability density function (pdf) and the cumulative distribution function (cdf). The maximum likelihood estimation method is applied to estimate the stated distribution parameters. To assess and investigate the efficacy of estimators in terms of bias, variance, and mean square error (MSE), a simulation study was conducted. Lastly, the effectiveness of the stated distribution is proven by actual data sets. [ABSTRACT FROM AUTHOR]