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In this paper, we consider transmuted generalized Lindley distribution, obtained via the quadratic rank transmutation map under the Lindley distribution. This distribution exhibits, in addition to decreasing, increasing and bathtub hazard rates, depending on its parameters, also unimodal hazard rate shape. A comprehensive mathematical treatment of this distribution is provided. Expressions for the moment generating function, moments, order statistics, residual life and reversed failure rate function are derived. The model parameters are estimated by the maximum likelihood method. A simulation study is performed to verify the behavior of the estimation procedure in terms of mean square errors and coverage probability. Global and local influence diagnostic procedures are provided. We then analyse a real data set on time-up-to-cure of patients treated with a triazole antifungal drug in an intensive care unit in Brazil.

revista de matemática e estatística

THE TRANSMUTED GENERALIZED LINDLEY DISTRIBUTION: PROPERTIES AND AN APPLICATION TO A DATA SET ON TIME-UP-TO-CURE OF PATIENTS TREATED WITH A TRIAZOLE ANTIFUNGAL DRUG IN AN INTENSIVE CARE UNIT