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Generalized X-Exponential Bathtub Shaped Failure Rate Distribution

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Abstract

Generalized Lindley, Generalized Gamma, Exponentiated Weibull and X-Exponential distributions are proposed for modelling lifetime data having bathtub shaped failure rate model. These distributions have several desirable properties. In this paper, we introduce a new distribution which generalizes the X-Exponential distribution. Several properties of the distribution are derived including the hazard rate function, moments, moment generating function etc. Moreover, we discussed the maximum likelihood estimation of this distribution. The usefulness of the new distribution is illustrated by means of two real data set. We hope that the new distribution will serve as an alternative model to bathtub models available in the literature.

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Acknowledgements

The authors are grateful to the Editor in Chief and anonymous referees for their constructive comments and suggestions which resulted in significant improvement in the manuscript.

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Authors and Affiliations

  1. Department of Statistics, St.Thomas College (Autonomous), Thrissur, Kerala, India

    V. M. Chacko & K. S. Deepthi

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  1. V. M. Chacko
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  2. K. S. Deepthi
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Correspondence to V. M. Chacko.

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Chacko, V.M., Deepthi, K.S. Generalized X-Exponential Bathtub Shaped Failure Rate Distribution. J Indian Soc Probab Stat 20, 157–171 (2019). https://doi.org/10.1007/s41096-019-00066-7

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  • DOI: https://doi.org/10.1007/s41096-019-00066-7

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