Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions

Abstract

This article introduces a two-parameter exponentiated Teissier distribution. It is the main advantage of the distribution to have increasing, decreasing and bathtub shapes for its hazard rate function. The expressions of the ordinary moments, identifiability, quantiles, moments of order statistics, mean residual life function and entropy measure are derived. The skewness and kurtosis of the distribution are explored using the quantiles. In order to study two independent random variables, stress–strength reliability and stochastic orderings are discussed. Estimators based on likelihood, least squares, weighted least squares and product spacings are constructed for estimating the unknown parameters of the distribution. An algorithm is presented for random sample generation from the distribution. Simulation experiments are conducted to compare the performances of the considered estimators of the parameters and percentiles. Three sets of real data are fitted by using the proposed distribution over the competing distributions.

Keywords:

• Exponentiated family
• Teissier distribution
• identifiability
• moments
• mean residual life
• estimation

AMS Subject Classifications:

• 60E05
• 62F10
• 62F99

This article refers to:

A note on the unimodality and log-concavity of the exponentiated Teissier distribution

This article responds to:

Discussion comments on “Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions”

Acknowledgements

Authors are grateful to the editor-in chief, associated editor of the Journal and anonymous referees for their careful reading of the manuscript and constructive suggestions, which had notably improved the earlier version of the manuscript. Authors also greatly acknowledge the financial support from Science and Engineering Research Board, Department of Science & Technology, Govt. of India, under the scheme Early Career Research Award (file no.: ECR/2017/002416).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Authors also greatly acknowledge the financial support from Science and Engineering Research Board, Department of Science & Technology, Govt. of India, under the scheme Early Career Research Award (file no.: ECR/2017/002416).