Open Access

ARTICLE

Inverse Length Biased Maxwell Distribution: Statistical Inference with an Application

by Amer Ibrahim Al-Omari¹, Ayed R.A. Alanzi^2,*

1 Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan
2 Department of Mathematics, College of Science and Human Studies at Hotat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia

* Corresponding Author: Ayed R.A. Alanzi. Email:

Computer Systems Science and Engineering 2021, 39(1), 147-164. https://doi.org/10.32604/csse.2021.017362

Received 28 January 2021; Accepted 14 March 2021; Issue published 10 June 2021

Abstract

In this paper, we suggested and studied the inverse length biased Maxell distribution (ILBMD) as a new continuous distribution of one parameter. The ILBMD is obtained by considering the inverse transformation technique of the Maxwell length biased distribution. Statistical characteristics of the ILBMD such as the moments, moment generating function, mode, quantile function, the coefficient of variation, coefficient of skewness, Moors and Bowley measures of kurtosis and skewness , stochastic ordering, stress-strength reliability, and mean deviations are obtained. In addition, the Bonferroni and Lorenz curves, Gini index, the reliability function, the hazard rate function, the reverse hazard rate function, the odds function, and the distributions of order statistics for the ILBMD, are presented. The ILBMD parameter is estimated using the maximum likelihood method, the method of moments, the maximum product of spacing technique, the ordinary and weight least square procedures, and the Cramer-Von-Mises methods. The Fishers information, as well as the Rényi and q-entropies, are derived. To investigate the usefulness of the proposed lifetime distribution and to illustrate the purpose of the study, a real dataset of the relief times of 20 patients receiving an analgesic is used.

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Keywords

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