Research Article
BibTex RIS Cite
Year 2021, , 899 - 914, 01.09.2021
https://doi.org/10.35378/gujs.721816

Abstract

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).

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

Year 2021, , 899 - 914, 01.09.2021
https://doi.org/10.35378/gujs.721816

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.

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).
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Statistics
Authors

Festus Opone 0000-0002-8414-4700

Blessing Iwerumor

Publication Date September 1, 2021
Published in Issue Year 2021

Cite

APA Opone, F., & Iwerumor, B. (2021). A New Marshall-Olkin Extended Family of Distributions with Bounded Support. Gazi University Journal of Science, 34(3), 899-914. https://doi.org/10.35378/gujs.721816
AMA Opone F, Iwerumor B. A New Marshall-Olkin Extended Family of Distributions with Bounded Support. Gazi University Journal of Science. September 2021;34(3):899-914. doi:10.35378/gujs.721816
Chicago Opone, Festus, and Blessing Iwerumor. “A New Marshall-Olkin Extended Family of Distributions With Bounded Support”. Gazi University Journal of Science 34, no. 3 (September 2021): 899-914. https://doi.org/10.35378/gujs.721816.
EndNote Opone F, Iwerumor B (September 1, 2021) A New Marshall-Olkin Extended Family of Distributions with Bounded Support. Gazi University Journal of Science 34 3 899–914.
IEEE F. Opone and B. Iwerumor, “A New Marshall-Olkin Extended Family of Distributions with Bounded Support”, Gazi University Journal of Science, vol. 34, no. 3, pp. 899–914, 2021, doi: 10.35378/gujs.721816.
ISNAD Opone, Festus - Iwerumor, Blessing. “A New Marshall-Olkin Extended Family of Distributions With Bounded Support”. Gazi University Journal of Science 34/3 (September 2021), 899-914. https://doi.org/10.35378/gujs.721816.
JAMA Opone F, Iwerumor B. A New Marshall-Olkin Extended Family of Distributions with Bounded Support. Gazi University Journal of Science. 2021;34:899–914.
MLA Opone, Festus and Blessing Iwerumor. “A New Marshall-Olkin Extended Family of Distributions With Bounded Support”. Gazi University Journal of Science, vol. 34, no. 3, 2021, pp. 899-14, doi:10.35378/gujs.721816.
Vancouver Opone F, Iwerumor B. A New Marshall-Olkin Extended Family of Distributions with Bounded Support. Gazi University Journal of Science. 2021;34(3):899-914.