A new class of weighted exponential distributions

Abstract

Introducing a shape parameter to an exponential model is nothing new. There are many ways to introduce a shape parameter to an exponential distribution. The different methods may result in variety of weighted exponential (WE) distributions. In this article, we have introduced a shape parameter to an exponential model using the idea of Azzalini, which results in a new class of WE distributions. This new WE model has the probability density function (PDF) whose shape is very close to the shape of the PDFS of Weibull, gamma or generalized exponential distributions. Therefore, this model can be used as an alternative to any of these distributions. It is observed that this model can also be obtained as a hidden truncation model. Different properties of this new model have been discussed and compared with the corresponding properties of well-known distributions. Two data sets have been analysed for illustrative purposes and it is observed that in both the cases it fits better than Weibull, gamma or generalized exponential distributions.

Keywords:

• hazard function
• log-concavity
• RR₂ ordering
• maximum likelihood estimators
• moment estimators
• Fisher information
• moment generating function

Acknowledgements

The authors would like to thank two anonymous referees for their valuable comments. Part of the work of the first author was supported by a grant from the Natural Sciences and Engineering Research Council, CANADA and part of the work of the second author was supported by a grant from the Department of Science and Technology, Government of India.