New Generalized Odd Fréchet-G (NGOF-G) Family of Distribution with Statistical Properties and Applications
DOI:
https://doi.org/10.56919/usci.2323.016Keywords:
New Odd Fréchet-G Family, Moments, Hazard functions, Maximum Likelihood, Monte Carlo SimulationsAbstract
The distribution theory literature contains recent types of parametric distributional models that have been successfully used in the past and whose goodness of fit is sufficient only for certain datasets, suggesting further attention to accommodate a wider range of real-world datasets, for more adaptability, efficiency, and applications. This study aims to develop an extended Fréchet-G family of distributions and study their mathematical properties. The method of Alzaatreh is employed in developing a new lifetime continuous probability distribution called the new Generalized Odd Fréchet-G Family of Distribution. The developed distribution is flexible for studying positive real-life datasets. The statistical properties related to this family are obtained. The parameters of the family were estimated by using a technique of maximum likelihood. A New Generalized Odd Fréchet-Weibull model is introduced. This distribution was fitted with a set of lifetime data. A Monte Carlo simulation is applied to test the consistency of the estimated parameters of this distribution in terms of their bias and mean squared error with a comparison of M.L.E and the maximum product spacing (MPS). The findings of the Monte Carlo simulation show that the M.L.E method is the best technique for estimating the parameter of New Generalized Odd Frechet-Weibull distribution than the M.PS method. The findings of the application on the data set produce a higher flexibility than some of the competing distributions. In general, our new distributions serve as a viable alternative to other distributions available in the literature for modelling positive data.
References
Ahmad, Z., Ampadu, C. B., Hamedani, G. G., Jamal, F., & Nasir, M. A. (2019). The new exponentiated TX class of distributions: properties, characterizations and application. Pakistan Journal of Statistics and Operation Research, 941-962. https://doi.org/10.18187/pjsor.v15i4.3019
Ahmad, Z., Elgarhy, M., & Hamedani, G. G. (2018). A new Weibull-X family of distributions: properties, characterizations and applications. Journal of Statistical Distributions and Applications, 5(1), 1-18. https://doi.org/10.1186/s40488-018-0087-6
Ahmed, Haitham, Cordeiro, Edwin and Zohdy (2016). "The Weibull Fréchet distribution and its applications". Journal of Applied Statistics, http://dx.doi.org/10.1080/02664763.2016.114 2945
Alexander, C., Cordeiro, G. M., Ortega, E. M., & Sarabia, J. M. (2012). Generalized beta- generated distributions. Computational Statistics & Data Analysis, 56(6), 1880-1897. https://doi.org/10.1016/j.csda.2011.11.015
Alizadeh, M., Ghosh, I., Yousof, H. M., Rasekhi, M., & Hamedani, G. G. (2017). The generalized odd generalized exponential family of distributions: Properties, characterizations and application. Journal of Data Science, 15(3), 443-465. https://doi.org/10.6339/JDS.201707_15(3).0005
Alzaatreh, A., Lee, C., Famoye, F. (2013b). A new method for generating families of continuous distributions. Metron, 71, 63-79. https://doi.org/10.1007/s40300-013-0007-y
Alzaghal, A., Famoye, F. and Lee, C. (2013): Exponentiated T-X family of distributions with some applications. International Journal of Statistics and Probability, 2(3), 31-49. https://doi.org/10.5539/ijsp.v2n3p31
Bourguignon, M., Silva, R. B. and Cordeiro, G. M. (2014). The Weibull-G family of a probability distribution. Journal of Data Science, 12, 53-68. https://doi.org/10.6339/JDS.201401_12(1).0004
Chukwu A. U., & Ogunde A. A., (2015). On the Beta Mekaham Distribution and Its Application. American Journal of Mathematics and Statistics 2015, 5(3): 137-143.
Cordeiro, G. M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E. M. M., & Altun, E. (2017). The generalized odd log-logistic family of distributions: properties, regression models and applications. Journal of Statistical Computation and Simulation, 87(5), 908-932. https://doi.org/10.1080/00949655.2016.1238088
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. https://doi.org/10.6339/JDS.201301_11(1).0001. https://doi.org/10.6339/JDS.2013.11(1).1086
De Gusmao, F. R., Ortega, E. M., & Cordeiro, G. M. (2011). The generalized inverse Weibull distribution Statistical Papers, 52, 591-619. https://doi.org/10.1007/s00362-009-0271-3
Deepshikha, D.; Bhatia, D.; Bhupen, k. B.; Bhupen, B. (2021). "Some Properties on Fréchet- Weibull Distribution with Application to Real Life Data. Mathematics and Statistics. 9(1): 8-15. https://doi.org/10.13189/ms.2021.090102
Eugene, N., Lee, C. and Famoye, F. (2002). Beta-Normal Distribution and It Applications. Communications in Statistics: Theory and Methods, 31: 497-512. https://doi.org/10.1081/STA-120003130
Falgore, J. Y., & Doguwa, S. I. (2020). The inverse Lomax-g family with application to breaking strength data. Asian Journal of Probability and Statistics, 49-60. https://doi.org/10.9734/ajpas/2020/v8i230204
Fisher, R. A.; Tippett, L. H. C. (1928). "Limiting forms of the frequency distribution of the largest and smallest member of a sample". Proceedings of the Cambridge Philosophical Society. 24 (2): 180-190. https://doi.org/10.1017/S0305004100015681
Fisher, R. A.; Tippett, L. H. C. (1928). "Limiting forms of the frequency distribution of the largest and smallest member of a sample". Proceedings of the Cambridge Philosophical Society. 24 (2): 180-190. https://doi.org/10.1017/S0305004100015681
Gumbel, E. J. (1958). Statistics of Extremes. New York: Columbia University Press. OCLC 180577. https://doi.org/10.7312/gumb92958
Gupta, R. C., Gupta, P. L. and Gupta, R. D. (1998). Modelling failure time data by Lehmann alternatives. Communications in Statistics - Theory and Methods 27, 887-904. https://doi.org/10.1080/03610929808832134
Haight, Frank A. (1967), Handbook of the Poisson distribution, New York, NY, USA: John Wiley & Sons, ISBN 978-0-471-33932-8
Jamal, F., Ahmad, Z., Ampadu, C. B., Hamedani, G. G., & Nasir, M. A. (2019). The New Exponentiated TX Class of Distributions: Properties, Characterizations, and Application, Pakistan Journal of Statistics and Operation Research, 941–962. https://doi.org/10.18187/pjsor.v15i4.3019
Jamal, F., Arslan Nasir, M., Ozel, G., Elgarhy, M., & Mamode Khan, N. (2019). Generalized Inverted Kumaraswamy Generated Family of Distributions: Theory and Applications, Journal of Applied Statistics, 46(16), 2927–2944. https://doi.org/10.1080/02664763.2019.1623867
Khan M.S.; Pasha G.R.; Pasha A.H. (February 2008). "Theoretical Analysis of Inverse Weibull Distribution". WSEAS Transactions on Mathematics. 7 (2). pp. 30-38.
Marganpoor, S., Ranjbar, V., Alizadeh, M., & Abdollahnezhad, K. (2020). Generalised odd Frechet family of distributions: properties and applications. Statistics in Transition new series, 21(3), 109-128. https://doi.org/10.21307/stattrans-2020-047
Montfort, M. A. On testing that the distribution of extremes is of type I when type II is the alternative, 11, 421-427, 1970. https://doi.org/10.1016/0022-1694(70)90006-5
Oguntunde P. E., A. O. Adejumo& K. A. Adepoju (2016). Assessing the Flexibility of the Exponentiated Generalized Exponential Distribution, Pacific Journal of Science and Technology, 17(1), 49-57
Tahir, M. H., Cordeiro, G. M., Alizadeh, M., Mansoor, M., Zubair, M., & Hamedani, G. G. (2015). The odd generalized exponential family of distributions with applications. Journal of Statistical Distributions and Applications, 2(1), 1-28. https://doi.org/10.1186/s40488-014-0024-2
Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M., & Zubair, M. (2016). The logistic-X family of distributions and its applications. Communications in statistics-Theory and methods, 45(24), 7326-7349. https://doi.org/10.1080/03610926.2014.980516
Tahir, M. H., Zubair, M., Cordeiro, G. M., Alzaatreh, A. and Mansoor, M. (2016). The Poisson-X Family of Distributions. Journal of Statistical Computation and Simulation, 86, 2901- 2921. https://doi.org/10.1080/00949655.2016.1138224
Tahir, M. H., Zubair, M., Mansoor, M., Cordeiro, G. M., ALİZADEHK, M., & Hamedani, G. (2016). A new Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics, 45(2), 629-647. https://doi.org/10.15672/HJMS.2015579686
Thomas W. Keelin (2016) The Meta log Distributions. Decision Analysis 13(4):243-277. http://dx.doi.org/10.1287/deca.2016.0338. https://doi.org/10.1287/deca.2016.0338
Torabi, H. and Montazari, N.H. (2012). The gamma-uniform distribution and its application. Kybernetika 48:16-30.
Torabi, H., & Bagheri, F. L. (2010). Estimation of Parameters for an Extended Generalized Half Logistic Distribution Based on Complete and Censored Data
Ul Haq, M. A., & Elgarhy, M. (2018). The odd Frѐchet-G family of probability distributions. Journal of Statistics Applications & Probability, 7(1), 189-203. https://doi.org/10.18576/jsap/070117
Usman A., Doguwa S. I. S., Alhaji B. B., and Imam A. T. A New Weibull- Odd Frechet G Family of Distributions. Transactions of the Nigerian Association of Mathematical Physics Volume 14, (January - March 2021 Issue), pp133 -142
Yahaya, A., & Doguwa, S. I. S. 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), pp143-154© Trans. of NAMP on
Yousof, H. M., Rasekhi, M., Afify, A. Z., Ghosh, I., Alizadeh, M., & Hamedani, G. G. (2017). The Beta Weibull-G Family of Distributions: Theory, Characterizations and Applications. Pakistan Journal of Statistics, 33(2). https://doi.org/10.18187/pjsor.v14i4.2527
Zografos, K., & Balakrishnan, N. (2009). On Families of Beta-Generalized Gamma-Generated Distributions and Associated Inference, Statistical Methodology, 6(4), 344–362. https://doi.org/10.1016/j.stamet.2008.12.003
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 UMYU Scientifica
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
