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The unit Muth distribution: statistical properties and applications

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Abstract

This paper introduces a bounded probability distribution which is derived from the Muth distribution. The main statistical properties are studied and analytical expressions are provided for the moments, incomplete moments, inverse of the cumulative distribution function, extropy, Lorentz and Bonferroni curves, among others. Moreover, it possesses both monotone and non-monotone hazard rate functions so the new distribution is rich enough to model real data. Different estimation methods are applied to estimate the parameters of the model and a Monte Carlo simulation study assesses their performances. The usefulness in practical applications is illustrated using two real data sets and the results show that the proposed distribution provides better fits than other competing distributions commonly used to model data with bounded support.

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Acknowledgements

Research of Pedro Jodrá has been partially funded by Diputación General de Aragón –Grupo E24-17R– and ERDF funds.

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Authors and Affiliations

  1. Department of Statistics, Goverment College for Women, Trivandrum, Kerala, 695 014, India

    R. Maya

  2. Departamento de Métodos Estadísticos, EINA, Universidad de Zaragoza, 50018, Zaragoza, Spain

    P. Jodrá

  3. Department of Statistics, Cochin University of Science and Technology, Cochin, Kerala, 682 022, India

    M. R. Irshad & A. Krishna

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Correspondence to M. R. Irshad.

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Maya, R., Jodrá, P., Irshad, M.R. et al. The unit Muth distribution: statistical properties and applications. Ricerche mat (2022). https://doi.org/10.1007/s11587-022-00703-7

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