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In this paper, a new family of distribution is introduced to model the lifetime of a system consisting of series and parallel systems having a random number of components. As a submodel, the Weibull baseline is considered in detail and some basic mathematical properties are examined such as quantile function and moments. Several estimation methods are considered to estimate the parameters of the proposed distribution. A comprehensive Monte Carlo simulation study is designed to assess the performance of these estimators in terms of mean squared errors. Two numerical examples are also provided to illustrate the flexibility of the proposed distribution. The proposed model reveals to be better than other current models considered in the examples based on the Akaike information criterion and some goodness-of-fit statistics.

This study introduces a new lifetime distribution called the transmuted lower record type inverse Rayleigh which extends the inverse Rayleigh distribution and has the potential to model the recovery times of Covid-19 patients.The new distribution is obtained using the distributions of the first two lower record statistics of the inverse Rayleigh distribution. We discuss some statistical inferences and mathematical properties of the suggested distribution. We examine some characteristics of the proposed distribution such as density shape, hazard function,moments, moment generating function, incomplete moments,Rényi entropy, order statistics, stochastic ordering. We consider five estimation methods such as maximum likelihood, least squares, weighted least squares, Anderson-Darling, Cramér-von Mises for the point estimation of the proposed distribution. Then, a comprehensive Monte Carlo simulation study is carried out to assess the risk behavior of the examined estimators. We provide two real data applications to illustrate the fitting ability of the proposed model, and compare its fit with competitor ones. Unlike many previously proposed distributions, the introduced distribution in this paper has modeled the recovery times of Covid-19 patients.

This paper introduces a new lifetime distribution by mixing the first two lower record values and various distributional properties are examined. Statistical inference on distribution parameters are discussed with five estimators. A Monte Carlo simulation study is carried out to evaluate the risk behavior of these estimators for different sample of sizes. The distribution modeling analysis is provided based on real data to demonstrate the fitting ability of the proposed model. In addition, a lifetime regression model is described by re-parameterization on the log lifetimes. The superiority of proposed regression model is revealed in well-known models.