Estimation with Modified Power Function Distribution Based on Order Statistics with Application to Evaporation Data

Devendra Kumar (), Maneesh Kumar and J. P. Singh Joorel
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Devendra Kumar: Central University of Haryana
Maneesh Kumar: Central University of Haryana
J. P. Singh Joorel: University of Jammu

Annals of Data Science, 2022, vol. 9, issue 4, No 4, 723-748

Abstract: Abstract The modified power function distribution is an important distribution for analyzing the lifetime data, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub shaped failure rate. In this paper, we derive the exact explicit expressions for the single and double (product) of order statistics from the modified power function distribution. By using these relations, we have tabulated the expected values, second moments, variances and covariances of order statistics from samples of sizes up to 10 for various values of the parameters. Also, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on Type-II right-censored samples. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to one real data set.

Keywords: Modified power function; Order statistics; Single moment; Double moment; Type-II right censoring; Best linear unbiased estimator (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s40745-020-00244-6

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