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Construction of an Alternative Bivariate Distribution with Discrete Modified Weibull as Marginals

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Abstract

An alternative version of bivariate discrete Weibull distribution with marginal densities as discrete modified Weibull distribution is constructed. Certain important properties of the model viz. joint distribution function, joint probability mass function, marginal distributions, moment generating function and conditional distributions are derived so as to enable this model in the practical application of reliability analysis such as risk modelling and shock modelling. The parameters of the model are estimated through method of maximum likelihood estimation and compared the performance of our model with other existing bivariate models. The usefulness of the model is illustrated through some real life data sets. A simulation study is carried out using Monte Carlo simulation and computed the bias of various estimators of our model.

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Acknowledgements

The authors would like to express their sincere thanks to the Editor-in-Chief and the anonymous Referees for their valuable comments and suggestions. The first author extends her acknowledgements to the financial assistance from the UGC, New Delhi, in the form of Junior Research Fellowship (JRF).

Funding

This work is supported by University Grand Commission

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Author notes

  1. Both the authors, N. Nimna Beegum and D. S. Shibu, contributed equally to this work.

Authors and Affiliations

  1. Department of Statistics, University College, Palayam, Kerala, India

    N. Nimna Beegum & D. S. Shibu

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  1. N. Nimna Beegum
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  2. D. S. Shibu
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Correspondence to N. Nimna Beegum.

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Nimna Beegum, N., Shibu, D.S. Construction of an Alternative Bivariate Distribution with Discrete Modified Weibull as Marginals. J Indian Soc Probab Stat 23, 337–358 (2022). https://doi.org/10.1007/s41096-022-00138-1

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  • DOI: https://doi.org/10.1007/s41096-022-00138-1

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