Development of Rayleigh-Exponentiated Odd Generalized-Weibull Distribution with Properties
DOI:
https://doi.org/10.70882/josrar.2025.v2i2.68Keywords:
REOGWD, Exponentiated distribution, Maximum likelihood estimation, Hazard function, Survival functionAbstract
We propose a new family of distributions called the Rayleigh-Exponentiated odd Generalized-Weibull Distribution with two positive parameters, which generalizes the Cordeiro and de Castro's family. Some special distributions in the new class are discussed. We derive the validity and some mathematical properties of the proposed distribution including explicit expressions for the quantile function, ordinary moments, Moment generating function, hazard and Survival function. The method of maximum likelihood is used to estimation of REOG-Weibull distributions. These functions are illustrated with graphs, since REOGWD was evident through graphics.
References
Abdulsalam, H., Abubakar, Y., & Dikko, H. G. (2021). On the properties and applications of a new extension of exponentiated rayleigh distribution. FUDMA Journal of Sciences, 5(2), 377-398.
Adamu, A., Yahaya, A., & Dikko, H. G. (2021). Applications of inverse Weibull rayleigh distribution to failure rates and vinyl chloride data sets. Fudma Journal of Sciences, 5(2), 89-99.
Akinsete, A., Lowe, D., & Nadarajah, S. (2008). The Beta-R distribution. Journal of Statistical Computation and Simulation, 78(12), 1105-1119.
Al-Babtain, A., Al-Zahem, A., Almutairi, M., & Al-Mosawi, A. (2020). Odd Generalized Weibull Distribution with Applications. Journal of Probability and Statistical Science, 18(1), 99-116.
Al-Hussaini, E. K., & Ahsanullah, M. (2015). Exponentiated distributions. Atlantis Studies in Probability and Statistics, 21.
Ali, M. M., Pal, M., & Woo, J. S. (2007). Some exponentiated distributions. Communications for Statistical Applications and Methods, 14(1), 93-109.
Almongy, H. M., Almetwally, E. M., Aljohani, H. M., Alghamdi, A. S., & Hafez, E. H. (2021). A new extended Rayleigh distribution with applications of COVID-19 data. Results in Physics, 23, 104012.
Al-Noor, N. H., & Assi, N. K. (2020, July). Rayleigh-Rayleigh distribution: properties and applications. In Journal of Physics: Conference Series (Vol. 1591, No. 1, p. 012038). IOP Publishing.
Alzaatreh, A., & Ghosh, I. (2015). On the Weibull-X family of distributions. Journal of statistical theory and applications, 14(2), 169-183.
Ateeq, K., Qasim, T. B., & Alvi, A. R. (2019). An extension of Rayleigh distribution and applications. Cogent Mathematics & Statistics, 6(1), 1622191.
Azzalini, A. (1985). A Class of Distributions which Includes the Normal Ones. Scandinavian Journal of Statistics, 12(2), 171-178.
Beckmann, P. (1964). Rayleigh distribution and its generalizations. Radio Sci. J. Res. NBS/USNC-URSI, 68(9), 927-932.
Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.
Cohen, A. C., & Whitten, B. J. (1988). Parameter Estimation in Reliability and Life Span Models. CRC Press.
Cooray, K. (2006). Generalization of the Weibull distribution: the odd Weibull family. Statistical Modelling, 6(3), 265-277.
Cordeiro, G. M., Afify, A. Z., Yousof, H. M., Pescim, R. R., & Aryal, G. R. (2017). The exponentiated Weibull-H family of distributions: Theory and Applications. Mediterranean Journal of Mathematics, 14, 1-22.
Cordeiro, G. M., M. Ortega, E. M., & Ramires, T. G. (2015). A new generalized Weibull family of distributions: mathematical properties and applications. Journal of Statistical Distributions and Applications, 2, 1-25.
Cordeiro, G. M., Ortega, E. M., & da Cunha, D. C. (2013). The exponentiated generalized class of distributions. Journal of data science, 11(1), 1-27.
de Andrade, T. A., Bourguignon, M., & Cordeiro, G. M. (2016). The exponentiated generalized extended exponential distribution. Journal of Data Science, 14(3), 393-413.
Dey, S., Dey, T., & Kundu, D. (2014). Two-parameter Rayleigh distribution: different methods of estimation. American Journal of Mathematical and Management Sciences, 33(1), 55-74.
Guerra, R. R., Peña-Ramírez, F. A., & Bourguignon, M. (2021). The unit extended Weibull families of distributions and its applications. Journal of Applied Statistics, 48(16), 3174-3192.
Gupta, R. C., Gupta, P. L., & Gupta, R. D. (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics-Theory and methods, 27(4), 887-904.
Gupta, R. D., & Kundu, D. (1999). Generalized Exponentiated Exponential Family: An Alternative to Exponential Distribution. Communications in Statistics Theory and Methods, 28(3), 785-800.
Gupta, R. D., & Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188.
Gupta, Rameshwar D., and Debasis Kundu. "Exponentiated exponential family: an alternative to gamma and Weibull distributions."Biometrical Journal: Journal of Mathematical Methods in Biosciences 43.1 (2001): 117-130.
Hoffman, D., & Karst, O. J. (1975). The theory of the Rayleigh distribution and some of its applications. Journal of Ship Research, 19(03), 172-191.
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Continuous Univariate Distributions (Vol. 1). John Wiley & Sons.
Klein, J. P., & Moeschberger, M. L. (2003). Survival Analysis: Techniques for Censored and Truncated Data. Springer.
Kundu, D., & Raqab, M. Z. (2005). Generalized Rayleigh distribution: different methods of estimations. Computational statistics & data analysis, 49(1), 187-200.
Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. John Wiley & Sons.
Lee, P. M. (2010). *Bayesian Statistics: An Introduction. Wiley.
Louzada-Neto, F., El-Bassiouni, M. Y., & Lemonte, A. J. (2001). Extended Weibull Family. Brazilian Journal of Probability and Statistics, 15(1), 45-66.
Marshall, A. W., & Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84(3), 641-652.
Mendenhall, W., Sincich, T., & Boudreau, N. S. (2016). Statistics for Engineering and the Sciences. CRC Press.
Merovci, F., & Elbatal, I. (2015). Weibull Rayleigh distribution: Theory and applications. Applied Mathematics & Information Sciences, 9(4), 2127.
Mudholkar, G. S., & Hutson, A. D. (1996). The Exponentiated Weibull Family: Some Properties and a Flood Data Application. Technometrics, 38(3), 260-272.
Mudholkar, G. S., & Kollia, G. D. (1994). Generalized Weibull family: a structural analysis. Communications in statistics-theory and methods, 23(4), 1149-1171.
Mudholkar, G. S., Srivastava, D. K., & Kollia, G. (1996). A Generalization of the Weibull Distribution with Applications. IEEE Transactions on Reliability, 45(2), 346-352.
Nadarajah, S. (2011). The exponentiated exponential distribution: a survey. AStA Advances in Statistical Analysis, 95, 219-251.
Nadarajah, S., & Kotz, S. (2006). The Exponentiated Gumbel Distribution. Journal of Applied Statistics, 33(1), 33-43.
Pal, M., Ali, M. M., & Woo, J. (2006). Exponentiated weibull distribution. Statistica, 66(2), 139-147.
Pham, H. (2006). Handbook of Reliability Engineering. Springer.
Raja, T. A., & Mir, A. H. (2011). On extension of some exponentiated distributions with application. International Journal of Contemporary Mathematical Sciences, 6(8), 393-400.
Rather, A. A., & Subramanian, C. (2020). A New Exponentiated Distribution with Engineering Science Applications. Journal of Statistics, Applications and Probability, 9(1), 127-137.
Rayleigh, L. (1880). On the resultant of a large number of vibrations of the same pitch and arbitrary phase. Philosophical Magazine, 10, 73-78.
Siddiqui, M. M. (1962). Some problems connected with Rayleigh distributions. Journal of Research of the National Bureau of Standards D, 66, 167-174.
Tahir, M. H., Zubair, M., Mansoor, M., Cordeiro, G. M., Alizadehk, M., & Hamedani, G. (2016). A new Weibull-G family of distributions. Hacettepe Journal of Mathematics and statistics, 45(2), 629-647.
Weibull, W. (1951). A Statistical Distribution Function of Wide Applicability. Journal of Applied Mechanics, 18(3), 293-297.
Xie, M., & Lai, C. D. (1995). Reliability Analysis Using an Additive Weibull Model with Bathtub-shaped Failure Rate Function. Reliability Engineering & System Safety, 52(1), 87-93.
Yahaya, A., & Doguwa, S. I. S. (2021). On Theoretical Study of Rayleigh-Exponentiated Odd Generalized-X Family of Distributions. Transactions of the Nigerian Association of Mathematical Physics Volume 14, (January-March, 2021 Issue), pp. 143–154© Trans. of NAMP.
Yahaya, A., & Doguwa, S. I. S. (2022) On Rayleigh-Exponentiated Odd Generalized-Pareto Distribution with its Applications.
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Copyright (c) 2025 Abubakar Salisu, Abdulhamid Ado Osi, Musa Uba Muhammad, Abubakar Yahaya, Muhammad Haladu (Author)
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