This article suggests a new statistical distribution using cubic rank transmutation map. Various statistical estimators of unknown parameters of this distribution are derived. A Monte Carlo simulation study based on bias and mean square error criteria of this estimator is conducted.

In this study, we introduce a new lifetime distribution by using quadratic rank transmutation map. The some properties of this new distribution is provided. Furthermore, the parameters of this new distribution are estimated by the maximum likelihood method. The performances of the estimates are examined according to bias and mean squared errors (MSEs) criteria through a Monte Carlo simulation study. Finally, two applications with real data are presented to evaluate the fits of introduced distribution.

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Akash distribution is a mixture of an exponential distribution and a gamma distribution with certain mixing proportions. Although the maximum likelihood estimation method has been proposed for the Akash distribution, there is no comprehensive comparison of different methods of estimation in the literature. This study provides five different methods of estimation, such as maximum likelihood, least-squares, weighted least-squares, Anderson-Darling, and Crámer-von-Mises for Akash distribution. We consider a comprehensive Monte Carlo simulation study to compare the performances of these methods via the biases and meansquared errors of these estimators. Also, a real data application is performed.

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