A Class of Regression Models for Parallel and Series Systems with a Random Number of Components

• Activity Number: 349
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 11:15 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Silvia L.P. Ferrari*+ and Alice L. Morais
• Companies: University of São Paulo and University of São Paulo
• Keywords: Weibull distribution ; quantile inference ; regression model ; systems with random number of components

Abstract

We extend the Weibull power series (WPS) class of distributions and named the new class as extended Weibull power series (EWPS) class of distributions. The EWPS distributions are related to series and parallel systems with a random number of components, whereas the WPS distributions (Morais & Barreto-Souza, Comput. Stat. Data Anal., 2011) are related to series systems only. Unlike the WPS distributions, for which the Weibull is a limiting special case, the Weibull law is a particular case of the EWPS distributions. We prove that the distributions in this class are identifiable under a simple assumption. We also prove stochastic and hazard rate order results and highlight that the shapes of the EWPS distributions are more flexible than those of the WPS distributions. We define a regression model for the EWPS response random variable to model a scale parameter and its quantiles. We prove the consistency and asymptotic normality of the maximum likelihood estimator. Although the construction of this class is motivated by series and parallel systems, the EWPS distributions are suitable for modeling a wide range of positive data sets. An application to a real data set is presented.