Quantum mechanics

Natural exponential family

Statistics

Applied mathematics

Skew

Gamma distribution

Distribution (mathematics)

Telecommunications

Power (physics)

Computer science

Physics

Mathematics

Exponential distribution

Exponential function

Mathematical analysis

Weibull distribution

Reliability (semiconductor)

Exponential family

Artificial intelligence

Class (philosophy)

Generalization

Symmetry

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications