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The location-scale family of generalized Maxwell distributions: theory and applications to annual rainfall records

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Abstract

This article introduces a location-scale family of Maxwell distributions for modelling the total annual rainfall of India from 1901 to 2014. It is shown that the distribution is quite flexible for modelling increasing and bathtub shaped failure rate data sets. The basic properties including moments, entropy, identifiability, conditional moments, mean residual life and stochastic ordering are explicitly derived here. Maximum likelihood estimation along with asymptotic confidence intervals are discussed. The score functions are also provided to compute the asymptotic confidence intervals of the parameters. The applicability of the distribution for Rainfall data is assessed and compared with 3-parameter Weibull and Gamma distributions. It is observed from the goodness-of-fit criteria that the rainfall data set is nicely fitted by the proposed distribution.

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Acknowledgements

Authors thank Editor-in-chief, associate editor of the journal and anonymous reviewers for their constructive suggestions on the earlier draft of the manuscript. Dr. Vikas Kumar Sharma greatly acknowledges the fi nancial 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).

Funding

Funding was provided by Science and Engineering Research Board, Department of Science & Technology, Govt. of India (Grant No. ECR/2017/002416).

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Authors and Affiliations

  1. Department of Mathematics, Institute of Infrastructure Technology, Research and Management (IITRAM), Ahmedabad, India

    Sudhanshu V. Singh & Vikas Kumar Sharma

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  1. Sudhanshu V. Singh
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  2. Vikas Kumar Sharma
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Correspondence to Vikas Kumar Sharma.

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Singh, S.V., Sharma, V.K. The location-scale family of generalized Maxwell distributions: theory and applications to annual rainfall records. Int J Syst Assur Eng Manag 10, 1505–1515 (2019). https://doi.org/10.1007/s13198-019-00900-y

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  • DOI: https://doi.org/10.1007/s13198-019-00900-y

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