Abstract
This paper introduces a new four-parameter lifetime model called the odd log-logistic Dagum distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some structural properties of the model odd log-logistic Dagum such as order statistics and incomplete moments. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling real data.
Highlights
In 1977, the Professor Camilo Dagum has derived the distribution function, which is called Dagum distribution, from a set of assumptions characterizing the observed regularities in the income distributions from both developed and developing countries (Dagum 1977)
Domma (2002) showed that the hazard rate of the Dagum distribution, according to the values of parameters, can be monotonically decreasing, upside-down bathtub, and, nally, bathtub upside-down bathtub. This particular exibility of the hazard rate has led to several authors apply the Dagum distribution in dierent elds, such as survival analysis and reliability theory
We investigate mathematical properties of the odd log-logistic Dagum (OLLDa) distribution including ordinary and incomplete moments, probability weighted moments (PWMs) and order statistics
Summary
In 1977, the Professor Camilo Dagum has derived the distribution function, which is called Dagum distribution, from a set of assumptions characterizing the observed regularities in the income distributions from both developed and developing countries (Dagum 1977). Gleaton & Lynch (2006) dened a new transformation of distribution function called the odd log-logistic-G (OLL-G) family with one additional shape parameter α > 0 by the cumulative distribution function (cdf). If we are interested in modeling the randomness of the odds by the log-logistic pdf r(t) = α tα−1/(1+tα) (for t > 0), the cdf of X is given by. The aim of this paper is to dene and study a new lifetime model called the odd log-logistic Dagum (OLLDa) distribution. Based on the odd log-logistic-G (OLL-G) family of distributions, we construct the four-parameter OLLDa model and give a comprehensive description of some of its mathematical properties in order that it will attract wider applications in reliability, engineering and other areas of research.
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