The Nakagami–Weibull distribution in modeling real-life data

İbrahim Abdullahi

doi:10.17776/csj.828677

EN

The Nakagami–Weibull distribution in modeling real-life data

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.

Details

Primary Language

English

Subjects

Statistics

Journal Section

Research Article

Authors

İbrahim Abdullahi ^*
0000-0002-7280-3035
Nigeria

Publication Date

June 30, 2021

Submission Date

November 21, 2020

Acceptance Date

April 28, 2021

Published in Issue

Year 2021 Volume: 42 Number: 2

DOI

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

IZ

https://izlik.org/JA64AP45UC

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

AMA

1.Abdullahi İ. The Nakagami–Weibull distribution in modeling real-life data. CSJ. 2021;42(2):422-433. doi:10.17776/csj.828677

Chicago

Abdullahi, İbrahim. 2021. “The Nakagami–Weibull Distribution in Modeling Real-Life Data”. Cumhuriyet Science Journal 42 (2): 422-33. https://doi.org/10.17776/csj.828677.

EndNote

Abdullahi İ (June 1, 2021) The Nakagami–Weibull distribution in modeling real-life data. Cumhuriyet Science Journal 42 2 422–433.

IEEE

[1]İ. Abdullahi, “The Nakagami–Weibull distribution in modeling real-life data”, CSJ, vol. 42, no. 2, pp. 422–433, June 2021, doi: 10.17776/csj.828677.

ISNAD

Abdullahi, İbrahim. “The Nakagami–Weibull Distribution in Modeling Real-Life Data”. Cumhuriyet Science Journal 42/2 (June 1, 2021): 422-433. https://doi.org/10.17776/csj.828677.

JAMA

1.Abdullahi İ. The Nakagami–Weibull distribution in modeling real-life data. CSJ. 2021;42:422–433.

MLA

Abdullahi, İbrahim. “The Nakagami–Weibull Distribution in Modeling Real-Life Data”. Cumhuriyet Science Journal, vol. 42, no. 2, June 2021, pp. 422-33, doi:10.17776/csj.828677.

Vancouver

1.İbrahim Abdullahi. The Nakagami–Weibull distribution in modeling real-life data. CSJ. 2021 Jun. 1;42(2):422-33. doi:10.17776/csj.828677

Cited By

Theory, simulation, and application of the entropy transformation of the Chen distribution to enhance interdisciplinary data analysis

Journal of Radiation Research and Applied Sciences

https://doi.org/10.1016/j.jrras.2025.101472

New Nakagami Weibull Distribution: A New Approach with Data Applications

WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL

https://doi.org/10.37394/23203.2025.20.44

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December