Abstract
In this paper, we proposed the Poisson-Weibull distribution for the modeling of survival data. The motivation to study this model since, in addition to generalizing the Weibull distribution, which is widely used in several areas of knowledge among them the Survival and Reliability analysis, it presents great exibility in the forms of the hazard function. The Poisson-Weibull distribution was created in a composition of discrete and continuous distributions where there is no information about which factor was responsible for the component failure, only the minimum lifetime value among all risks is observed. The maximum likelihood approach was used to estimate the parameters of the model. Also was conducted a simulation study to examine the mean, the bias, and the root of the mean square error of the maximum likelihood estimates of the proposed model according to the censoring percentages and sample sizes. The model selection criteria were also applied, in addition to graphic techniques such as TTT-Plot and Kaplan-Meier. Application to the real data set was used to illustrate the usefulnessof the distribution.
Highlights
In several applications of statistics, the response variable consists of the time until the occurrence interest event, and this time is generally called failure time or survival time
In animal science, according to Cardoso et al (2009), several characteristics of importance economic show censored data, that is, that are not fully observed for all animals at the time of genetic evaluation. Characteristics such as longevity, prolificacy, and total female productivity are examples of censored data, because many animals are still reproducing at the time of evaluation and, only the lower limit of their phenotypic value is known
The choice of PoissonWeibull distribution (PW) model, in addition to generalizing the Weibull distribution, which is one of the most used distributions in the area of survival and recent years is applied to data in the unit interval (MAZUCHELI et al, 2020), presents great flexibility in the forms of the hazard function
Summary
In several applications of statistics, the response variable consists of the time until the occurrence interest event, and this time is generally called failure time or survival time. It is considered that both the number and the identification of the components that caused the failure are not observable, but only the value of the minimum lifetime among them, where the number of components follows a geometric distribution and the time of duration of each component follows an exponential distribution. The choice of PW model, in addition to generalizing the Weibull distribution, which is one of the most used distributions in the area of survival and recent years is applied to data in the unit interval (MAZUCHELI et al, 2020), presents great flexibility in the forms of the hazard function. Applications of the PW distribution in survival studies for data without censored observations were investigated by Bereta et al (2011)
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