Topp–Leone normal distribution with application to increasing failure rate data

ABSTRACT

In this article, we proposed a new three-parameter probability distribution, called Topp–Leone normal, for modelling increasing failure rate data. The distribution is obtained by using Topp–Leone-X family of distributions with normal as a baseline model. The basic properties including moments, quantile function, stochastic ordering and order statistics are derived here. The estimation of unknown parameters is approached by the method of maximum likelihood, least squares, weighted least squares and maximum product spacings. An extensive simulation study is carried out to compare the long-run performance of the estimators. Applicability of the distribution is illustrated by means of three real data analyses over existing distributions.

Keywords:

• Normal distribution
• Topp–Leone generated family
• hazard rate
• moments
• quantile function
• orderings
• order statistics
• maximum likelihood estimator
• maximum product spacing estimator
• least squares estimator
• weighted least squares estimator

AMS Subject Classifications:

• 60E05
• 62F10
• 62F99

Acknowledgements

Authors thank to Editor-in-chief, associate editor and anonymous reviewers for their constructive suggestions that greatly improved the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Vikas Kumar Sharma http://orcid.org/0000-0003-0169-4094