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Classical Inferences of Order Statistics for Inverted Modified Lindley Distribution with Applications

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Strength of Materials Aims and scope

Inverted modified Lindley distribution was developed without considering any special function or additional parameters in its formulation. This model provides better fit than exponential and Lindley distributions and it was suitable for modeling increasing, reverse bathtub (unimodal) and constant shaped hazard rate function. This article emphasize the estimation of a one-parameter inverted modified Lindley distribution by using order statistics. First, the explicit expressions for single and product moments of order statistics from this distribution are derived. We have also tabulated the first four inverse moments of order statistics for various values of the parameter. In the part of estimation, we first utilize the maximum likelihood (ML) estimator and approximate confidence interval to obtain the model parameter based on order statistics. Based on order statistics, a simulation study is carried out to check the efficiency of the estimator. Two real life data sets, have been analyzed for order statistics to demonstrate how the proposed methods may work in practice.

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Authors and Affiliations

  1. Department of Statistics, Central University of Haryana, Mahendergarh, India

    D. Kumar & P. Yadav

  2. Department Mathematics and Statistics, Vellore Institute of Technology, Vellore, India

    J. Kumar

Authors
  1. D. Kumar
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  2. P. Yadav
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  3. J. Kumar
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Correspondence to D. Kumar.

Additional information

Translated from Problemy Mitsnosti, No. 2, p. 122, March – April, 2023.

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Kumar, D., Yadav, P. & Kumar, J. Classical Inferences of Order Statistics for Inverted Modified Lindley Distribution with Applications. Strength Mater 55, 441–455 (2023). https://doi.org/10.1007/s11223-023-00537-0

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  • DOI: https://doi.org/10.1007/s11223-023-00537-0

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