New Generalized Odd Fréchet-G (NGOF-G) Family of Distribution with Statistical Properties and Applications

Authors

  • Ibrahim Abubakar Sadiq Department of Statistics, Ahmadu Bello University, Zaria https://orcid.org/0000-0002-2122-9344
  • Sani Ibrahim Doguwa Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria
  • Abubakar Yahaya Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria
  • Jamilu Garba Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria

DOI:

https://doi.org/10.56919/usci.2323.016

Keywords:

New Odd Fréchet-G Family, Moments, Hazard functions, Maximum Likelihood, Monte Carlo Simulations

Abstract

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

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Published

2023-09-30

How to Cite

Abubakar Sadiq, I., Doguwa, S. I., Yahaya, A., & Garba, J. (2023). New Generalized Odd Fréchet-G (NGOF-G) Family of Distribution with Statistical Properties and Applications. UMYU Scientifica, 2(3), 100–107. https://doi.org/10.56919/usci.2323.016