Abstract
In this paper, we introduce maximum likelihood and Bayesian parameter estimation for the exponentiated discrete Weibull (EDW) distribution in presence of randomly right censored data. We also consider the inclusion of a cure fraction in the model. The performance of the maximum likelihood estimation approach is assessed by conducting an extensive simulation study with different sample sizes and different values for the parameters of the EDW distribution. The usefuness of the proposed model is illustrated with two examples considering real data sets.
Highlights
Let T be a random variable denoting a survival time, and let t be an observation of T
In order to exemplify the application of the exponentiated discrete Weibull (EDW) model and to compare the results from the frequentist and Bayesian approaches, we simulate samples of size n = 50, 100, and 300 from the EDW distribution for (α, β, γ) equal to (a) (1.5, 2, 0.2), (b) (1, 1.5, 0.6), (c) (1, 3, 0.3), (d) (1.1, 0.8, 0.2), (e) (0.8, 0.4, 0.6), and (f) (2, 1, 0.15), according to the steps described in the subsection 2.5
We evaluate the maximum likelihood (ML) estimations of the parameters using the maxLik package of the R software (Henningsen and Toomet,2011) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization method (Broyden,1970; Fletcher,1970)
Summary
Let T be a random variable denoting a survival time, and let t be an observation of T. Weibull (EDW) distribution, introduced by Nekoukhou and Bidram(2015), has probability accumulated distribution function given by. The correspondent probability mass function (pmf ) is given by f (t) = P (T = t) = − 1 − θtα β , t ∈ N0, [1].
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