A new statistical distribution: cubic rank transmuted Kumaraswamy distribution and its properties

This article suggests a new statistical distribution named ʻCubic rank transmuted Kumaraswamy distribution’ using cubic rank transmutation map. Various statistical properties of this new distribution such as, hazard function and its graphics, moments, variance, coefficients of skewness and kurtosis, moment generating function and order statistics are examined. In estimation problem, the maximum likelihood 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. Also, this new distribution is compared with other well known distributions in terms of fitting to the total milk production proportion, operation and empirical datasets in previous studies.