A New Inverse Lomax Weibull-G Family of Distributions with Applications
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10.58578/kijst.v1i1.3721
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Abstract
The field of statistics is constantly evolving, and new approaches are being developed to model real-world datasets. Despite this, there are still many significant concerns surrounding real data that remain unresolved by existing approaches. One of the drawbacks of the Inverse Lomax distribution is that it belongs to the inverted family of distributions, which limits its application and makes it unsuitable for some situations. Based on these, a new family of distributions called Inverse Lomax Weibull G (ILWG) based on the Inverse Lomax-G and Weibull-G was proposed in this study. Some statistical properties of the family such as the quantile function, moments, and characteristic function were presented. Exponential distribution was used as a member of this family to demonstrate the applicability of the new family. Some statistical properties of the Inverse Lomax Weibull exponential distribution (ILWED) such as quantile function, moments, and characteristic function were demonstrated. ILWED's shapes can be right skewed and symmetric, as the case maybe. Sample quantiles were presented. A simulation study was also presented to explore the desirable properties of the ILWED. Lastly, an application to three (3) different datasets was demonstrated based on the ILWED.
Keywords:
Weibull; Inverse Lomax-G family; Exponential Distribution; New Weibull Inverse Lomax Distribution; Weibull-G
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Falgore, J. Y., Abubakar, Y., Doguwa, S. I., Mohammed, A. S., & Imam, A. T. (2024). A New Inverse Lomax Weibull-G Family of Distributions with Applications. Kwaghe International Journal of Sciences and Technology, 1(1), 586-609. https://doi.org/10.58578/kijst.v1i1.3721
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
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[24] Gupta, R. D., and Kundu, D. (2009). A new class of Weighted Exponential distributions, Statistics, 43 (6):621–634.
[25] Khan, M. S., King, R., and Hudson, I. L. (2017). Transmuted generalized Exponential distribution: a generalization of the Exponential distribution with applications to survival data, Communications in Statistics-Simulation and Computation, 46 (6):4377–4398.
[26] Zubair, M., Alzaatreh, A., Tahir, M., Mansoor, M., and Mustafa, M. (2018). A generalization of the Exponential distribution and its applications on modeling skewed data, Statistical Theory and Related Fields, 2 (1):68–79.
[27] Usman, L., Jose, M., and Veena, G. (2020). A review on recent generalizations of exponential distribution, Biomedical and Biostatistics International Journal 9:152–156.
[28] Chesneau, C., Kumar, V., Khetan, M., and Arshad, M. (2022). On a modified Weighted Exponential distribution with applications, Mathematical and Computational Applications, 27 (1): 1-20.
[29] Chesneau, C., Tomy, L., and Jose, M. (2024). On a new two-parameter weighted Exponential distribution and its application to the Covid-19 and censored data, Thailand Statistician, 22 (1): 17–30.
[30] Maxwell, O., Kayode, A. A., Onyedikachi, I. P., Obi-Okpala, C. I., and Victor, E. U. (2019). Usefull generalization of the Inverse Lomax distribution: Statistical properties and application to lifetime data, American Journal of Biomedical Science and Research, 6 (3): 258–265.
[31] Alzaatreh, A., Lee, C., and Famoye, F. (2013). A new method for generating families of continuous distributions, Metron, 71 (1): 63–79.
[32] Dodge, Y. (2008). The Concise Encyclopedia of Statistics, Springer Science and Business Media.
[33] Mahdavi, A., and Kundu, D. (2017). A new method for generating distributions with an application to Exponential distribution, Communications in Statistics-Theory and Methods, 46 (13): 6543-6557.
[34] Chaudhary, A. K., Telee, L. B. S., and Kumar, V. (2022). Inverse exponentiated odd Lomax Exponential distribution, Nepalese Journal of Statistics, 6: 29–50.
[35] Nasiru, S. (2018). Extended odd Frechet-G family of distributions, Journal of Probability and Statistics, 2018 (1): 1–12.
[36] Alshanbari, H. M., Odhah, o. H., Almetwally, E. M., Hussam, E., Kilai, M., and El-Bagoury, A. A. H. (2022). Novel Type I half logistic Burr-Weibull distribution: Application to Covid-19 data, Computational and Mathematical Methods in Medicine, 2022 (1): 1444859.
[37] El-Damrawy, H. (2024). The Beta-Truncated Lomax distribution with Communications data, Delta Journal of Science, 48 (1): 135–144.
[38] Gul, A., Sandhu, A. J., Farooq, M., Adil, M., Hassan, Y., and Khan, F. (2023). Half Logistic-Truncated Exponential distribution, Characteristic and Applications, 18 (11): e0285992.
[2] Abdullah, M. M., and Masmoudi, A. (2023). Modeling real-life dataset with a novel G family of continuous probability distributions: statistical properties, and copulas, Pakistan Journal of Statistics and Operation Research, 719-746.
[3] Arif, M., Khan, D. M., Aamir, M., Khalil, U., Bantan, R. A., and Elgarhy, M. (2022). Modeling Covid-19 with a novel extended exponentiated class of distributions, Journal of Mathematics, 1-14.
[4] Al-Omari, A. I., Hassan, A. S., Alotaibi, N., Shrahili, M., and Nagy, H. F. (2021). Reliability estimation of Inverse Lomax distribution using extreme ranked set sampling, Advances in Mathematical Physics, 1–12.
[5] Ogunde, A. A., Chukwu, A. U., and Oseghale, I. O. (2023). The kumaraswamy generalized inverse lomax distribution and applications to reliability and survival data, Scientific African 19: e01483.
[6] Falgore, J. Y. and Doguwa, S. I. (2022). On new Weibull Inverse Lomax distribution with applications, Baghdad Science Journal, 19 (3): 0528–0535.
[7] Shama, M. S., Alharthi, A. S., Almulhim, F. A., Gemeay, A. M., Meraou, M. A., Mustafa, > S., Hussam, E., and Aljohani, H. M. (2023). Modified generalized Weibull distribution: theory and applications, Scientific Reports 13 (1): 12828.
[8] Algamal, Z. Y. and Basheer, G. (2021). Reliability estimation of three parameters Weibull distribution based on particle swarm optimization, Pakistan Journal of Statistics and Operation Research, 17 (1):35-42.
[9] Falgore, J. Y., Doguwa, S. I., and Isah, A. (2019). The Weibull-Inverse Lomax (WIL) distribution with application on Bladder Cancer, Biometric and Biostatistics International Journal 8(5): 195-202.
[10] Hassan, A. S. and Mohmed, R. E. (2019). Weibull Inverse Lomax Distribution, Pakistan Journal of Statistics and Operation Research, 15 (13): 587-603.
[11] Hussain, N. A., Doguwa, S. I., and Yahaya, A. (2020). The Weibull Power Lomax distribution: properties and application, Communication in Physical Sciences, 6(2): 869-881.
[12] Falgore, J. Y. and Doguwa, S. I. (2020a). Inverse Lomax-G family with application to Breaking Strength data, Asian Journal of Probability and Statistics, 8 (2):49–60.
[13] Falgore, J. Y. and Doguwa, S. I. (2020b). Inverse lomax-exponentiated-G (ILEG) family of distributions: properties and applications, Asian Journal of Probability and Statistics, 9 (4):48–64.
[14] Fayomi, A., Algarni, A., and Almarashi, A. M. (2021). Sine Inverse Lomax Generated family of distributions with applications, Mathematical Problems in Engineering, 2021 (1)1267420.
[15] Algarni, A., Almarashi, A. M., Jamal, F., Chesneau, C., and Elgarhy, M. (2021). Truncated Inverse Lomax Generated family of distributions with applications to Biomedical data, Journal of Medical Imaging and Health Informatics, 11 (9): 2425-2439.
[16] Bourguignon, M., Silva, R. B., and Cordeiro, G. M. (2022). The Weibull-G family of probability distributions, Journal of Data Science, 12 (1): 53-68.
[17] Tahir, M., Zubair, M., Mansoor, M., Cordeiro, G. M., Alizadeh, M., and Hamedani, G. (2016). A new Weibull G family of distributions, Hacettepe Journal of Mathematics and Statistics, 45 (2): 629–647.
[18] Korkmaz, M. C. (2018). A new family of the continuous distributions: the extended Weibull G family, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68 (1): 248–270.
[19] Alizadeh, M., Rasekhi, M., Yousof, H. M., and Hamedani, G. (2018). The transmuted Weibull-G family of distributions, Hacettepe Journal of Mathematics and Statistics, 47 (6): 1671-1689.
[20] Hassana, A. S., Shawkia, A., and Muhammeda, H. Z. (2022). Weighted Weibull-G family of distributions: theory and application in the analysis of renewable energy sources, Journal of Positive School Psychology, 6 (3):9201–9216.
[21] Zamanah, E., Nasiru, S., and Lugutera, A. (2022). Harmonic mixture Weibull-G family of distributions: properties, regression, and application to medical data, Computational and Mathematical Methods, 2022(1): 1–24.
[22] Tomy, L., Jose, M., and Veena, G. (2020). A review on recent generalizations of exponential distribution, Biomedical and Biostatistics International Journal 9:152–156.
[23] Gupta, R. D., and Kundu, D. (1999). Theory and Methods: Generalized Exponential distributions, Australian and New Zealand Journal of Statistics, 41 (2):173–188.
[24] Gupta, R. D., and Kundu, D. (2009). A new class of Weighted Exponential distributions, Statistics, 43 (6):621–634.
[25] Khan, M. S., King, R., and Hudson, I. L. (2017). Transmuted generalized Exponential distribution: a generalization of the Exponential distribution with applications to survival data, Communications in Statistics-Simulation and Computation, 46 (6):4377–4398.
[26] Zubair, M., Alzaatreh, A., Tahir, M., Mansoor, M., and Mustafa, M. (2018). A generalization of the Exponential distribution and its applications on modeling skewed data, Statistical Theory and Related Fields, 2 (1):68–79.
[27] Usman, L., Jose, M., and Veena, G. (2020). A review on recent generalizations of exponential distribution, Biomedical and Biostatistics International Journal 9:152–156.
[28] Chesneau, C., Kumar, V., Khetan, M., and Arshad, M. (2022). On a modified Weighted Exponential distribution with applications, Mathematical and Computational Applications, 27 (1): 1-20.
[29] Chesneau, C., Tomy, L., and Jose, M. (2024). On a new two-parameter weighted Exponential distribution and its application to the Covid-19 and censored data, Thailand Statistician, 22 (1): 17–30.
[30] Maxwell, O., Kayode, A. A., Onyedikachi, I. P., Obi-Okpala, C. I., and Victor, E. U. (2019). Usefull generalization of the Inverse Lomax distribution: Statistical properties and application to lifetime data, American Journal of Biomedical Science and Research, 6 (3): 258–265.
[31] Alzaatreh, A., Lee, C., and Famoye, F. (2013). A new method for generating families of continuous distributions, Metron, 71 (1): 63–79.
[32] Dodge, Y. (2008). The Concise Encyclopedia of Statistics, Springer Science and Business Media.
[33] Mahdavi, A., and Kundu, D. (2017). A new method for generating distributions with an application to Exponential distribution, Communications in Statistics-Theory and Methods, 46 (13): 6543-6557.
[34] Chaudhary, A. K., Telee, L. B. S., and Kumar, V. (2022). Inverse exponentiated odd Lomax Exponential distribution, Nepalese Journal of Statistics, 6: 29–50.
[35] Nasiru, S. (2018). Extended odd Frechet-G family of distributions, Journal of Probability and Statistics, 2018 (1): 1–12.
[36] Alshanbari, H. M., Odhah, o. H., Almetwally, E. M., Hussam, E., Kilai, M., and El-Bagoury, A. A. H. (2022). Novel Type I half logistic Burr-Weibull distribution: Application to Covid-19 data, Computational and Mathematical Methods in Medicine, 2022 (1): 1444859.
[37] El-Damrawy, H. (2024). The Beta-Truncated Lomax distribution with Communications data, Delta Journal of Science, 48 (1): 135–144.
[38] Gul, A., Sandhu, A. J., Farooq, M., Adil, M., Hassan, Y., and Khan, F. (2023). Half Logistic-Truncated Exponential distribution, Characteristic and Applications, 18 (11): e0285992.
