An extended Maxwell distribution: Properties and applications

ABSTRACT

In this article, we propose an extension of the Maxwell distribution, so-called the extended Maxwell distribution. This extension is evolved by using the Maxwell-X family of distributions and Weibull distribution. We study its fundamental properties such as hazard rate, moments, generating functions, skewness, kurtosis, stochastic ordering, conditional moments and moment generating function, hazard rate, mean and variance of the (reversed) residual life, reliability curves, entropy, etc. In estimation viewpoint, the maximum likelihood estimation of the unknown parameters of the distribution and asymptotic confidence intervals are discussed. We also obtain expected Fisher’s information matrix as well as discuss the existence and uniqueness of the maximum likelihood estimators. The EMa distribution and other competing distributions are fitted to two real datasets and it is shown that the distribution is a good competitor to the compared distributions.

KEYWORDS:

• Hazard rate
• Maximum likelihood estimation
• Maxwell distribution
• Maxwell-X family
• Moments
• Residual life

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 62F10

Acknowledgments

Authors would like to thank editor-in-chief Professor N. Balakrishnan, and anonymous associate editor and referee for their constructive suggestions that greatly improved the last version of this manuscript. Authors owe special thanks to Professor Umesh Singh and Professor Sanjay Kumar Singh (Department of Statistics, Banaras Hindu University, Varanasi, India) for their discussion and suggestion to the content of the manuscript.