Abstract
This paper further develops the statistical inference procedure of the exponentiated discrete Weibull distribution (EDW) for data with the presence of censoring. This generalization of the discrete Weibull distribution has the advantage of being suitable to model non-monotone failure rates, such as those with bathtub and unimodal distributions. Inferences about EDW distribution are presented using both frequentist and bayesian approaches. In addition, the classical Likelihood Ratio Test and a Full Bayesian Significance Test (FBST) were performed to test the parameters of EDW distribution. The method presented is applied to simulated data and illustrated with a real dataset regarding patients diagnosed with head and neck cancer.
Highlights
The Weibull distribution is widely used to model survival data
An alternative way to find the EDW is first to exponentiated the continuous Weibull distribution, obtaining the exponentiated Weibull distribution proposed by Mudholkar and Srivastava (1993), and to discretize the exponentiated continuous Weibull to obtain the exponentiated discrete Weibull distribution
We performed hypothesis testing of the parameters of the EDW model by the full bayesian significance test (FBST), which is based on the e-value
Summary
The Weibull distribution is widely used to model survival data. The Weibull distribution and its generalizations have been applied over the years in survival analysis when the data are continuous. In some cases the data are discrete This can arise, for example, when the survival time is measured in months, cycles or counts. It is not always acceptable to use a continuous model to analyze discrete data. New families of distributions for continuous data have been proposed based on modifications of the Weibull distribution to deal with bathtubshaped or unimodal failure rates. Inferences about the parameters of the exponentiated discrete Weibull distribution (EDW) have only been presented for uncensored data. This paper formulates the EDW model in a context of survival analysis, allowing the presence of censored data in the inference process. All the simulations and estimates were carried out using the free R software (R CORE TEAM, 2019)
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