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Year 2021, Volume: 42 Issue: 2, 422 - 433, 30.06.2021

İbrahim Abdullahi

https://doi.org/10.17776/csj.828677

Abstract

References

  • [1] Nicholas E, Carl L, and Felix F. Beta-normal distribution and its applications, Communications in Statistics-Theory and methods, 31(4) (2002) 497-512.
  • [2] Gauss MC, Edwin MMO, and Daniel CC da C. The exponentiated generalized class of distributions, Journal of Data Science, 11(1) (2013) 1-27.
  • [3] Mohammed E and Amal H. Exponentiated weibull weibull distribution: Statistical properties and applications, Gazi University Journal of Science, 32(2) (2019) 616-635.
  • [4] Olanrewaju IS and Kazeem AA. On the beta-nakagami distribution, Progress in Applied Mathematics, 5(1) (2013) 49-58.
  • [5] Marcelo B., Rodrigo B.S., Gauss M.C., The weibull-g family of probability distributions, Journal of Data Science, 12(1) (2014) 53-68.
  • [6] Oguntunde PE, Adejumo AO, and Owoloko EA. Exponential Inverse Exponential (EIE) Distribution with Applications to Lifetime Data, Asian Journal of Scientific Research, 10 (2017) 169-177.
  • [7] Laba H and Subrata C. Beta generated kumaraswamy-g and other new families of distributions. arXiv preprint arXiv (2016) 1603.00634.
  • [8] Gauss MC, Morad A, and Edwin MMO. The Exponentiated Half-Logistic Family of Distributions: Properties and Applications, Journal of Probability and Statistics, vol. 2014 (2014) ID 864396, 21. Available at: https://doi.org/10.1155/2014/864396.
  • [9] Amal SH and Saeed EH. A new family of additive weibull-generated distributions, International Journal of Mathematics And its Applications, 4(2) (2016) 151–164.
  • [10] Rodrigo RP, Gauss MC, Clarice GBD, Edwin MMO, and Saralees N. The new class of kummer beta generalized distributions, SORT-Statistics and Operations Research Transactions, 36(2) (2012) 153-180.
  • [11] Saliou D and Christophe C. The generalized odd inverted exponential-g family of distributions: properties and applications, Eurasian Bulletin of Mathematics (ISSN: 2687-5632), 2(3) (2019) 86-110.
  • [12] Ahmed Z.A., Gauss C., Farrukh J, Mohamed E, and Mohamed N. The marshall-olkin odd burr iii-g family of distributions: Theory, estimation and applications, Available at: https://hal.archives-ouvertes.fr/hal-02376067. Retrieved November 22, 2019.
  • [13] Bistoon H, Mahmoud A, and Morad A. The generalized odd gamma-g family of distributions: properties and applications, Austrian Journal of Statistics, 47(2) (2018) 69-89.
  • [14] Abdullahi̇, İ , Job, O . A new family of odd generalized Nakagami (Nak-G) distributions, Turkish Journal of Science , 5 (2) (2020) 85-101.
  • [15] Zenga, M. Inequality curve and inequality index based on the ratios between lower and upper arithmetic means, Statistica e Applicazioni 4, (2007) 3–27.
  • [16] George C., Roger L.B., Statistical inference, 2nd ed. Australia ; Pacific Grove, CA : Thomson Learning, (2002).
  • [17] Arslan MN, Muhammad HT, Christophe C, Farrukh J, and Akbar MAS. The odds generalized gamma-g family of distributions: Properties, regressions and applications, Statistica, 80(1) (2020) 3-38.
  • [18] Oguntunde PE, Balogun OS, Okagbue HI, and Bishop SA. The weibull exponential distribution: Its properties and applications, Journal of Applied Sciences, 15(11) (2015) 1305-1311.
  • [19] Michele DN and Padgett WJ. A bootstrap control chart for weibull percentiles, Quality and reliability engineering international, 22(2) (2006) 141-151.
  • [20] Gauss MC and Artur JL. The β-birnbaum-saunders distribution: an improved distribution for fatigue life modeling, Computational Statistics & Data Analysis, 55(3) (2011) 1445-1461.
  • [21] Amal HS, Mohammed AE, and Mohammed S. Type ii half logistic family of distributions with applications, Pakistan Journal of Statistics and Operation Research, (2017) 245-264.
  • [22] Amal SH,Abd-Elfattah AM, and Asmaa HM. The complementary exponentiated inverted weibull power series family of distributions and its applications, Journal of Advances in Mathematics and Computer Science, (2016) 1-20.

The Nakagami–Weibull distribution in modeling real-life data

Year 2021, Volume: 42 Issue: 2, 422 - 433, 30.06.2021

İbrahim Abdullahi

https://doi.org/10.17776/csj.828677

Abstract

In this article, a four-parameter Nakagami Weibull distributions (NW) is proposed. We study a few statistical properties such as quantile function, moments, moment generating function, entropy, and order statistics have been derived. The maximum likelihood estimate is used to estimate the parameter of the NW distribution. We fit the proposed NW distribution to a real-life data set to examine its potential and flexibility. Our findings showed that the NW distribution performs much better than its competitors, with favorable comparisons to existing distributions in terms of goodness-of-fit.

Keywords

Nakagami Weibull Moment Entropy Quantile function

References

  • [1] Nicholas E, Carl L, and Felix F. Beta-normal distribution and its applications, Communications in Statistics-Theory and methods, 31(4) (2002) 497-512.
  • [2] Gauss MC, Edwin MMO, and Daniel CC da C. The exponentiated generalized class of distributions, Journal of Data Science, 11(1) (2013) 1-27.
  • [3] Mohammed E and Amal H. Exponentiated weibull weibull distribution: Statistical properties and applications, Gazi University Journal of Science, 32(2) (2019) 616-635.
  • [4] Olanrewaju IS and Kazeem AA. On the beta-nakagami distribution, Progress in Applied Mathematics, 5(1) (2013) 49-58.
  • [5] Marcelo B., Rodrigo B.S., Gauss M.C., The weibull-g family of probability distributions, Journal of Data Science, 12(1) (2014) 53-68.
  • [6] Oguntunde PE, Adejumo AO, and Owoloko EA. Exponential Inverse Exponential (EIE) Distribution with Applications to Lifetime Data, Asian Journal of Scientific Research, 10 (2017) 169-177.
  • [7] Laba H and Subrata C. Beta generated kumaraswamy-g and other new families of distributions. arXiv preprint arXiv (2016) 1603.00634.
  • [8] Gauss MC, Morad A, and Edwin MMO. The Exponentiated Half-Logistic Family of Distributions: Properties and Applications, Journal of Probability and Statistics, vol. 2014 (2014) ID 864396, 21. Available at: https://doi.org/10.1155/2014/864396.
  • [9] Amal SH and Saeed EH. A new family of additive weibull-generated distributions, International Journal of Mathematics And its Applications, 4(2) (2016) 151–164.
  • [10] Rodrigo RP, Gauss MC, Clarice GBD, Edwin MMO, and Saralees N. The new class of kummer beta generalized distributions, SORT-Statistics and Operations Research Transactions, 36(2) (2012) 153-180.
  • [11] Saliou D and Christophe C. The generalized odd inverted exponential-g family of distributions: properties and applications, Eurasian Bulletin of Mathematics (ISSN: 2687-5632), 2(3) (2019) 86-110.
  • [12] Ahmed Z.A., Gauss C., Farrukh J, Mohamed E, and Mohamed N. The marshall-olkin odd burr iii-g family of distributions: Theory, estimation and applications, Available at: https://hal.archives-ouvertes.fr/hal-02376067. Retrieved November 22, 2019.
  • [13] Bistoon H, Mahmoud A, and Morad A. The generalized odd gamma-g family of distributions: properties and applications, Austrian Journal of Statistics, 47(2) (2018) 69-89.
  • [14] Abdullahi̇, İ , Job, O . A new family of odd generalized Nakagami (Nak-G) distributions, Turkish Journal of Science , 5 (2) (2020) 85-101.
  • [15] Zenga, M. Inequality curve and inequality index based on the ratios between lower and upper arithmetic means, Statistica e Applicazioni 4, (2007) 3–27.
  • [16] George C., Roger L.B., Statistical inference, 2nd ed. Australia ; Pacific Grove, CA : Thomson Learning, (2002).
  • [17] Arslan MN, Muhammad HT, Christophe C, Farrukh J, and Akbar MAS. The odds generalized gamma-g family of distributions: Properties, regressions and applications, Statistica, 80(1) (2020) 3-38.
  • [18] Oguntunde PE, Balogun OS, Okagbue HI, and Bishop SA. The weibull exponential distribution: Its properties and applications, Journal of Applied Sciences, 15(11) (2015) 1305-1311.
  • [19] Michele DN and Padgett WJ. A bootstrap control chart for weibull percentiles, Quality and reliability engineering international, 22(2) (2006) 141-151.
  • [20] Gauss MC and Artur JL. The β-birnbaum-saunders distribution: an improved distribution for fatigue life modeling, Computational Statistics & Data Analysis, 55(3) (2011) 1445-1461.
  • [21] Amal HS, Mohammed AE, and Mohammed S. Type ii half logistic family of distributions with applications, Pakistan Journal of Statistics and Operation Research, (2017) 245-264.
  • [22] Amal SH,Abd-Elfattah AM, and Asmaa HM. The complementary exponentiated inverted weibull power series family of distributions and its applications, Journal of Advances in Mathematics and Computer Science, (2016) 1-20.
There are 22 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Natural Sciences
Authors

İbrahim Abdullahi 0000-0002-7280-3035

Publication Date June 30, 2021
Submission Date November 21, 2020
Acceptance Date April 28, 2021
Published in Issue Year 2021Volume: 42 Issue: 2

Cite

APA Abdullahi, İ. (2021). The Nakagami–Weibull distribution in modeling real-life data. Cumhuriyet Science Journal, 42(2), 422-433. https://doi.org/10.17776/csj.828677