Abstract
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.
Highlights
In many applied sciences such as medicine, engineering and finance, amongst others, modeling and analyzing lifetime data is crucial
Granzotto and Louzada (2015) considered a new lifetime distribution by using a quadratic rank transmutation map in order to add a new parameter to the log-logistic distribution
By using the Propositions 5.1 and 5.2, the joint distribution of the the ith and jth order statistics can be obtained from transmuted generalized Lindley distribution and it is given by fi::j:n(xi, xj ) = C [F (xi)]i−1 [F − F (xi)]j−i−1 [1 − F]n−j f (xi)f
Summary
In many applied sciences such as medicine, engineering and finance, amongst others, modeling and analyzing lifetime data is crucial. We consider a real data on time-up-to-cure of patients treated with a triazole antifungal drug in an intensive care unit. Our data set consists of time-up-to-cure of 54 patients treated in 2010 with this drug in an ICU at University Hospital, in Maringa city, Parana State, Brazil. We consider a new lifetime distribution by transmuting and compounding the generalized Lindley distribution, hereafter Transmuted Generalized Lindley (TGL) distribution It is the functional composition of a cumulative distribution function on a distribution with the inverse cumulative distribution (quantile) function of a non-Gaussian distribution (SHAW; BUCKLEY, 2007).
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