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The Reflected-Shifted-Truncated Lomax Distribution: Associated Inference with Applications

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Abstract

In health related studies, we sometimes come across left-skewed heavy-tailed survival data and vary often the probability distributions proposed in the literature to fit the model of such survival data is not adequate. In this article, we explore a new probability density function with bounded domain. The new distribution arises from the Lomax distribution proposed by Lomax (J Am Stat Assoc 49:847–852, 1954). The new transformed model, called the reflected-shifted-truncated Lomax (RSTL) distribution can be used to model left skewed data. It presents the advantage of not including any special function in its formulation. We provide a comprehensive treatment of general mathematical and statistical properties of this distribution. We estimate the model parameters by maximum likelihood methods based on complete and right censored data. To assess the performance of the maximum likelihood estimators, we conduct a simulation study with varying sample sizes. The flexibility and better fitness of the new family, is demonstrated by providing well-known examples that involve complete and right censored data. Using information theoretic criteria, we compare the RSTL distribution to the Exponential, Generalized F, Generalized Gamma, Gompertz, Log-logistic, Log-normal, Rayleigh, Weibull and reflected-shifted-truncated gamma (RSTG) distributions in two negatively skewed real data sets: complete (uncensored) burial data and right censored diabetic data. Our study suggests that the RSTL distribution works better than the aforementioned nine distributions based on four different information theoretic criteria.

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Acknowledgements

We would like to thank the Editor-in-Chief, associate editor and two referees for useful comments and suggestions that have significantly improved this article.

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Authors and Affiliations

  1. Department of Statistics, St. Anthony’s College, Shillong, Meghalaya, India

    Sanku Dey

  2. Department of Statistics, Bartin University, Bartin, 74100, Turkey

    Emrah Altun

  3. Department of Statistics, Central University of Haryana, Haryana, India

    Devendra Kumar

  4. Department of Mathematics and Statistics, University of North Carolina, Wilmington, NC, USA

    Indranil Ghosh

Authors
  1. Sanku Dey
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  2. Emrah Altun
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  3. Devendra Kumar
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  4. Indranil Ghosh
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Correspondence to Devendra Kumar.

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The authors declare no conflict of interest.

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The datasets used in this paper are provided within the main body of the manuscript.

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All the authors contributed equally to this work.

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Dey, S., Altun, E., Kumar, D. et al. The Reflected-Shifted-Truncated Lomax Distribution: Associated Inference with Applications. Ann. Data. Sci. 10, 805–828 (2023). https://doi.org/10.1007/s40745-021-00340-1

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  • DOI: https://doi.org/10.1007/s40745-021-00340-1

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