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On the asymptotic behaviour of the joint distribution of the maxima and minima of observations, when the sample size is a random variable

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Abstract

In this paper, we obtain the asymptotic form of the joint distribution of maxima and minima of independent observations, when the sample size is a random variable. We also discuss the asymptotic distribution of the range.

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Acknowledgements

The author is very much thankful to the referee for a number of valuable suggestions, which have lead to a lot of improvement in the present version of the paper.

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The author declares that no financial support has been received from any funding agency, for this work.

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  1. Department of Studies in Statistics, University of Mysore, Manasagangotri, Mysuru, 570006, India

    R. Vasudeva

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  1. R. Vasudeva
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Correspondence to R. Vasudeva.

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Vasudeva, R. On the asymptotic behaviour of the joint distribution of the maxima and minima of observations, when the sample size is a random variable. Metrika (2023). https://doi.org/10.1007/s00184-023-00928-y

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  • DOI: https://doi.org/10.1007/s00184-023-00928-y

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