A Novel Area-Biased Distribution With Essential Statistical Properties

Asgar Ali¹ , Aafaq A. Rather² , Berihan R. Elemary³

1. Dept. of Statistics, K. K. Das College, Garia, Kolkatta-700084, India.
2. Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune-411004, India.
3. Dept. of Applied Mathematical and Statistics, Faculty of Commerce, Damietta University-34511, Egypt.

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.4 , pp.24-28, Aug-2024

Online published on Aug 31, 2024

Copyright © Asgar Ali, Aafaq A. Rather, Berihan R. Elemary . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we introduce a novel model called the area biased Transmuted Mukherjee-Islam (ABTMI) distribution, which generalizes the Transmuted Mukherjee-Islam distribution through an area biased transformation approach. We thoroughly explore the probability density function (PDF) and the cumulative distribution function (CDF) of the ATMI distribution. Additionally, we investigate the distinctive structural properties of the proposed model, including the survival function, conditional survival function, hazard function, cumulative hazard function, mean residual life, moments, moment generating function (MGF), characteristic function (CF), cumulant generating function (CGF), entropy measures, and Bonferroni and Lorenz curves. The model parameters are estimated using the maximum likelihood estimation method.

Key-Words / Index Term :
Transmuted Mukherjee-Islam distribution, Area biased distribution, Reliability analysis, Maximum likelihood estimator

References :
[1] R.A. Fisher, “The Effects of Methods of Ascertainment Upon the Estimation of Frequencies,” Annals of Eugenics, Issue 6, pp.13- 25, 1934.
[2] C.R. Rao, “On Discrete Distributions Arising Out of Method of Ascertainment, In Classical and Contagious Discrete,” G.P. Patiled; Pergamum Press and Statistical Publishing Society, Calcutta, pp.320-332, 1965.
[3] A.A. Rather, G. Ozel, “The Weighted Power Lindley Distribution with Applications on the Life Time Data,” Pakistan Journal of Statistics and Operation Research, Vol.16, Issue.2, pp. 225-237, 2020.
[4] A. Ahmad, A.A. Rather, Y.A. Tashkandy, M.E. Bakr, M.M.M. El-Din, A.M. Gemeay, E.M. Almetwally, M. Salem, “Deriving the New Cotangent Frechet Distribution With Real Data Analysis,” Alexandria Engineering Journal, Vol.105, Issue.10, pp.12-24, 2024. https://doi.org/10.1016/j.aej.2024.06.038
[5] D. Qayoom, A. A. Rather, “Weighted Transmuted Mukherjee-Islam Distribution with Statistical Properties,” Reliability: Theory and Applications, Vol.78, Issue.2, pp. 124-137, 2024.
[6] A. Ahmad, A.A. Rather, A.M. Gemeay, M. Nagy, L.P. Sapkota, A.H. Mansi, “Novel Sin-G Class of Distributions with an Illustration of Lomax Distribution: Properties and Data Analysis,” AIP Advances, Vol.14, pp.1-17, 2024.
[7] A.A. Rather, C. Subramanian, “Transmuted Mukherjee-Islam Failure Model,” Journal of Statistics Applications & Probability, Vol.7, Issue.2, pp.343-347, 2018.
[8] W.T. Shaw, I.R.C. Buckley, “The Alchemy of Probability Distributions: Beyond Gram-Charlier Expansions and A Skew-Kurtotic-Normal Distribution from A Rank Transmutation Map,” Research report, 2007.
[9] R. Alfred, “On Measures of Information and Entropy,” Proceedings of the fourth Berkeley Symposium on Mathematics, Statistics and Probability 1960. pp.547–561, 1961.
[10] C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics,”. Journal of Statistical Physics, Vol.52, Issue.1-2, pp.479–487, 1988.
[11] C.E. Bonferroni, “Elementi Di Statistica Generale, Seeber, Firenze,” 1930.
[12] M.O. Lorenz, “Methods of measuring the concentration of wealth,” Publications of the American Statistical Association, Vol.9, pp.209–219, 1905.