A New Marshall-Olkin Extended Family of Distributions with Bounded Support

Year 2021, Volume: 34 Issue: 3, 899 - 914, 01.09.2021

Festus Opone Blessing Iwerumor

https://doi.org/10.35378/gujs.721816

Cited By: 6

Abstract

This paper presents a new Marshall-Olkin extended family of distributions with bounded support. Some of the Mathematical properties of the proposed distribution were studied and the method of maximum likelihood estimation was employed to estimate the unknown parameters of the proposed distribution. A Monte Carlo simulation study was carried out to examine the asymptotic behaviour of the parameter estimates of the distribution.” Finally, two real data sets defined on a unit interval were used to show the applicability of the proposed distribution in analyzing real data sets.

Keywords

Marshall-Olkin, Topp-Leone distribution, Maximum likelihood, Estimate

References

• [1] Mudholkar, G. S., Srivastava, D. K., “Exponentiated Weibull family for analyzing bathtub failure rate data”. IEEE Transactions on Reliability, 42: 299-302, (1993).
• [2] Marshall A. W., Olkin I., “A New Method for Adding a Parameter to a Family of Distributions with Application to the Exponential and Weibull Families”. Biometrika, 84: 641-652, (1997).
• [3] Eugene, N., Lee, C., Famoye, F., “The beta-normal distribution and its Applications”. Communications in Statistics - Theory and Methods, 31(4): 497-512, (2002).
• [4] Alzaatreh, A., Lee, C., & Famoye, F., “T- Normal family of distributions: A new approach to generalize the normal distribution”. Journal of Statistical Distributions and Applications, 1(16): 1-18, (2014).
• [5] Ahmed, H. H., Bdair, O. M., Ahsanullah, M., “On Marshall-Olkin Extended Weibull Distribution”. Journal of Statistical Theory and Applications, 16(1): 1-17, (2017).
• [6] Ahsan ul Haq, M., Usman, R. M., Amer, S. H., Al-Omeri, I., “The Marshall-Olkin length-biased exponential distribution and its applications”. Journal of King Saud University – Science, 31: 246–251, (2019).
• [7] Al-Saiari, A. Y., Baharith, L. A., Mousa, S. A., “Marshall-Olkin Extended Burr Type XII Distribution”. International Journal of Statistics and Probability, 3(1): 78-84, (2014).
• [8] Gharib, M., Mohammed, B. I., Aghel, W. E. R., “Marshll–Olkin Extended Inverse Pareto Distribution and its Application”. International Journal of Statistics and Probability, 6(6): 71-84, (2017).
• [9] Ghitany, M. E. “Marshall-Olkin Extended Pareto Distribution and its application”. International Journal of Applied Mathematics, 18: 17-31, (2005).
• [10] Ghitany, M. E., Al-Awadhi, F. A., Alkhalfan, L. A., “Marshall-Olkin extended Lomax distribution and its application to censored data”. Communication in Statistics- Theory and Methods, 36: 1855-1866, (2007).
• [11] Ghitany, M. E., Al- Mutairi, D. K., Al- Awadhi, F. A., Al-Burais, M. M., “Marshall-Olkin extended Lindley distribution and its application”. International Journal Applied Mathematics, 25 (5): 709-721, (2012).
• [12] Tahir, M. H., Cordeiro, G. M., Alzaatreh, M. A., Zubair, M., “A New Generalized Family of Distributions from Bounded Support”. Journal of Data Science, 16(2): 251-276, (2018).
• [13] Topp, C. W., Leone, F. C., “A family of J-shaped frequency functions”. Journal of the American Statistical Association, 50: 209-219, (1955).
• [14] George, R., Thobias, S., “Marshall-Olkin Kumaraswamy Distribution”. International Mathematical Forum, 12(2): 47-69, (2017).
• [15] Ekhosuehi, N., Nzei, L.C., Opone, F.C,. “A New Mixture of Exponential-Gamma Distribution”. Gazi University Journal of Science, 33(2): 548-564, (2020)
• [16] Rényi, A., “On measure of entropy and information”. Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability 1, University of California Press, Berkeley, 547-561, (1961).
• [17] Golshani, L., Pasha, E., “Renyi entropy rate for Gaussian processes”. Information Sciences, 180: 1486-1491, (2010).
• [18] Kayal, S. & Kumar, S., “Estimating Renyi entropy of several exponential distributions under an asymmetric loss function”. Statistical Journal, 15(4): 501-522, (2017).
• [19] Obin, N. & Liuni, M., “On the generalization of Shannon entropy for speech recognition”. IEEE Workshop on Spoken Language Technology, Miami, USA, December 2-5: 97-102, (2012).
• [20] Cordeiro, G. M., Brito, R. S., “The Beta Power Distribution”. Brazilian Journal of Probability and Statistics, 26(1): 88-112, (2012).
• [21] Mazucheli, J., Menezes, F. A., Dey, S., “Unit-Gompertz Distribution with Applications”. Statistica, 79(1): 25-43, (2019).