Research Article
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Year 2023, Volume: 72 Issue: 4, 921 - 958, 29.12.2023
https://doi.org/10.31801/cfsuasmas.1195058

Abstract

References

  • Afify, A.Z., Gemeay, A.M., Ibrahim, N.A., The heavy-tailed exponential distribution: risk measures, estimation, and application to actuarial data, Mathematics, 8(8) (2020), 1276. https://doi.org/10.3390/math8081276
  • Ahn, S., Kim, J.H., Ramaswami, V., A new class of models for heavy-tailed distributions in finance and insurance risk, Insurance: Mathematics and Economics, 51(1) (2012), 43-52. https://doi.org/10.1016/j.insmatheco.2012.02.002
  • Akaike, H., A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19(6) (1974), 716–723. DOI:10.1109/TAC.1974.1100705
  • Al-Mofleh, H., Elgarhy, M., Afify, A., Zannon, M., Type II exponentiated half logistic generated family of distributions with applications, Electronic Journal of Applied Statistical Analysis, 13(2) (2020), 536-561. DOI:10.1285/i20705948v13n2p536
  • AL-Kazrajy, A.A., Comparative study of estimation methods of reliability with complete data using simulation (With Application), MSc thesis(2001), Mosul University, Iraq.
  • Alotaibi, N., Elbatal, I., Almetwally, E.M., Alyami, S.A., Al-Moisheer, A.S., Elgarhy, M., Truncated Cauchy power Weibull-G class of distributions: Bayesian and non-Bayesian inference modelling for COVID-19 and carbon fiber data, Mathematics, 10(9) (2022), 1565. https://doi.org/10.3390/math10091565
  • Alyami, S.A., Babu, M.G., Elbatal, I., Alotaibi, N., Elgarhy, M., Type II half-logistic odd Frechet class of distributions: Statistical theory and applications, Symmetry, 14(6) (2022), 1222. https://doi.org/10.3390/sym14061222
  • Anwar, A., Bibi, A., The half-logistic generalized Weibull distribution, Journal of Probability and Statistics, 2018 (2018), Article ID 8767826, 12 pages. https://doi.org/10.1155/2018/8767826
  • Benkhelifa, L., Alpha power Topp-Leone Weibull distribution: properties, characterizations, Regression modeling and applications, Journal of Statistics and Management Systems, 25(8) (2022), 1945-1970. https://doi.org/10.1080/09720510.2021.1995217
  • Bourguignon, M., Silva R. B., Cordeiro G. M., The Weibull-G family of probability distributions, Journal of Data Science, 12 (2014), 53-68.
  • Bozdogan, H., Model selection and Akaike’s information criterion (AIC): The general theory and its analytical extensions, Psychometrika, 52(3) (1987), 345-370. https://doi.org/10.1007/BF02294361
  • Chakravarti, I.M., Laha, R.G., Roy, J., Handbook of methods of applied statistics, Wiley Series in Probability and Mathematical Statistics, 1 (1967), 392-394. DOI: 1130000794121857024
  • Chen, G., Balakrishnan, N., A general purpose approximate goodness-of-fit test, Journal of Quality Technology, 27(2) (1995), 154-161. https://doi.org/10.1080/00224065.1995.11979578
  • Chipepa, F., Oluyede, B., Makubate, B., The odd generalized half-logistic Weibull-G family of distributions: Properties and applications, Journal of Statistical Modeling: Theory and Applications, 1(1) (2020), 65-89. DOI: 10.22034/JSMTA.2020.1904
  • Cordeiro, G. M. Ortega, E. M. M. & Nadarajaah, S., The Kumaraswamy Weibull distribution with application to failure data, Journal of the Franklin Institute, 347(8) (2010), 1399-1429. https://doi.org/10.1016/j.jfranklin.2010.06.010
  • Dhungana, G.P. and Kumar, V., Exponentiated odd Lomax exponential distribution with application to COVID-19 death cases of Nepal, PloS One, 17(6) (2022), https://doi.org/10.1371/journal.pone.0269450
  • Eghwerido, J.T., Agu, F.I., The shifted Gompertz-G family of distributions: properties and applications, Mathematica Slovaca, 71(5) (2021), 1291-1308. https://doi.org/10.1515/ms-2021-0053
  • Hamedani, G.G., Rasekhi, M., Najibi, S., Yousof, H.M., Alizadeh, M., Type II general exponential class of distributions, Pakistan Journal of Statistics and Operation Research, 15(2) (2019), 503-523. https://doi.org/10.18187/pjsor.v15i2.1699
  • Handique, L., Ahsan, A.L., Chakraborty, S., Generalized modified exponential-G family of distributions: its properties and applications, International Journal of Mathematics and Statistics, 21(1) (2020), 1-17.
  • Hussein, M., Elsayed, H., Cordeiro, G.M., A new family of continuous distributions: properties and estimation, Symmetry, 14(2) (2022), 276. https://doi.org/10.3390/sym14020276
  • Korkmaz, M.Ç., A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application, Journal of Applied Statistics, 47(12) (2020), 2097-2119. https://doi.org/10.1080/02664763.2019.1704701
  • Lee, E. T., & Wang, J., Statistical Methods for Survival Data Analysis, John Wiley & Sons, 2003.
  • Moakofi, T., Oluyede, B., Gabanakgosi, M., The Topp-Leone odd Burr III-G family of distributions: Model, properties and applications, Statistics, Optimization & Information Computing, 10(1) (2022), 236-262. https://doi.org/10.19139/soic-2310-5070-1135
  • Moakofi, T., Oluyede, B., Chipepa, F., Makubate, B., Odd power generalized Weibull-G family of distributions: Model, properties and applications, Journal of Statistical Modelling: Theory and Applications, 2(1) (2021), 121-142. DOI:10.22034/JSMTA.2021.2333
  • Nascimento, A.D., Silva, K.F., Cordeiro, G.M., Alizadeh, M., Yousof, H.M., Hamedani, G.G., The odd Nadarajah-Haghighi family of distributions: properties and applications, Studia Scientiarum Mathematicarum Hungarica, 56(2) (2019), 185-210. https://doi.org/10.1556/012.2019.56.2.1416
  • Oluyede, B., Chipepa, F., The Marshall-Olkin odd exponential half logistic-G family of distributions: Properties and applications, Statistics, Optimization & Information Computing, 11(2) (2021), 479-503. https://doi.org/10.19139/soic-2310-5070-938
  • Rannona, K., Oluyede, B., Chipepa, F., Makubate, B., The Marshall-Olkin-exponentiated odd exponential half logistic-G family of distributions with applications, Eurasian Bulletin of Mathematics, 4(3) (2022), 134-161.
  • Schwarz, Gideon E., Estimating the dimension of a model, Annals of Statistics, 6(2) (1978), 461–464. https://www.jstor.org/stable/2958889
  • Teamah, A.E.A., Elbanna, A.A., Gemeay, A.M., Heavy-tailed log-logistic distribution: Properties, risk measures and applications, Statistics, Optimization & Information Computing, 9(4) (2021), 910-941. https://doi.org/10.19139/soic-2310-5070-1220
  • Zhao, W., Khosa, S.K., Ahmad, Z., Aslam, M., Afify, A.Z., Type-I heavy-tailed family with applications in medicine, engineering and insurance, PloS One, 15(8) (2020). https://doi.org/10.1371/journal.pone.0237462
  • Zhao, J., Ahmad, Z., Mahmoudi, E., Hafez, E.H., Mohie El-Din, M.M., A new class of heavytailed distributions: Modeling and simulating actuarial measures, Complexity, 2021 (2021), https://doi.org/10.1155/2021/5580228

The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications

Year 2023, Volume: 72 Issue: 4, 921 - 958, 29.12.2023
https://doi.org/10.31801/cfsuasmas.1195058

Abstract

In this study, we propose a new heavy-tailed distribution, namely, the type I heavy-tailed odd power generalized Weibull-G family of distributions. Several statistical properties including hazard rate function, quantile function, moments, distribution of the order statistics and Renyi entropy are presented. Actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are also derived. To obtain the estimates of the parameters of the new family of distributions, we adopt the maximum likelihood estimation method and assess the consistency property via a Monte Carlo simulation. Finally, we illustrate the usefulness of the new family of distributions by analyzing four real life data sets from different fields such as insurance, engineering, bio-medical and environmental sciences.

References

  • Afify, A.Z., Gemeay, A.M., Ibrahim, N.A., The heavy-tailed exponential distribution: risk measures, estimation, and application to actuarial data, Mathematics, 8(8) (2020), 1276. https://doi.org/10.3390/math8081276
  • Ahn, S., Kim, J.H., Ramaswami, V., A new class of models for heavy-tailed distributions in finance and insurance risk, Insurance: Mathematics and Economics, 51(1) (2012), 43-52. https://doi.org/10.1016/j.insmatheco.2012.02.002
  • Akaike, H., A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19(6) (1974), 716–723. DOI:10.1109/TAC.1974.1100705
  • Al-Mofleh, H., Elgarhy, M., Afify, A., Zannon, M., Type II exponentiated half logistic generated family of distributions with applications, Electronic Journal of Applied Statistical Analysis, 13(2) (2020), 536-561. DOI:10.1285/i20705948v13n2p536
  • AL-Kazrajy, A.A., Comparative study of estimation methods of reliability with complete data using simulation (With Application), MSc thesis(2001), Mosul University, Iraq.
  • Alotaibi, N., Elbatal, I., Almetwally, E.M., Alyami, S.A., Al-Moisheer, A.S., Elgarhy, M., Truncated Cauchy power Weibull-G class of distributions: Bayesian and non-Bayesian inference modelling for COVID-19 and carbon fiber data, Mathematics, 10(9) (2022), 1565. https://doi.org/10.3390/math10091565
  • Alyami, S.A., Babu, M.G., Elbatal, I., Alotaibi, N., Elgarhy, M., Type II half-logistic odd Frechet class of distributions: Statistical theory and applications, Symmetry, 14(6) (2022), 1222. https://doi.org/10.3390/sym14061222
  • Anwar, A., Bibi, A., The half-logistic generalized Weibull distribution, Journal of Probability and Statistics, 2018 (2018), Article ID 8767826, 12 pages. https://doi.org/10.1155/2018/8767826
  • Benkhelifa, L., Alpha power Topp-Leone Weibull distribution: properties, characterizations, Regression modeling and applications, Journal of Statistics and Management Systems, 25(8) (2022), 1945-1970. https://doi.org/10.1080/09720510.2021.1995217
  • Bourguignon, M., Silva R. B., Cordeiro G. M., The Weibull-G family of probability distributions, Journal of Data Science, 12 (2014), 53-68.
  • Bozdogan, H., Model selection and Akaike’s information criterion (AIC): The general theory and its analytical extensions, Psychometrika, 52(3) (1987), 345-370. https://doi.org/10.1007/BF02294361
  • Chakravarti, I.M., Laha, R.G., Roy, J., Handbook of methods of applied statistics, Wiley Series in Probability and Mathematical Statistics, 1 (1967), 392-394. DOI: 1130000794121857024
  • Chen, G., Balakrishnan, N., A general purpose approximate goodness-of-fit test, Journal of Quality Technology, 27(2) (1995), 154-161. https://doi.org/10.1080/00224065.1995.11979578
  • Chipepa, F., Oluyede, B., Makubate, B., The odd generalized half-logistic Weibull-G family of distributions: Properties and applications, Journal of Statistical Modeling: Theory and Applications, 1(1) (2020), 65-89. DOI: 10.22034/JSMTA.2020.1904
  • Cordeiro, G. M. Ortega, E. M. M. & Nadarajaah, S., The Kumaraswamy Weibull distribution with application to failure data, Journal of the Franklin Institute, 347(8) (2010), 1399-1429. https://doi.org/10.1016/j.jfranklin.2010.06.010
  • Dhungana, G.P. and Kumar, V., Exponentiated odd Lomax exponential distribution with application to COVID-19 death cases of Nepal, PloS One, 17(6) (2022), https://doi.org/10.1371/journal.pone.0269450
  • Eghwerido, J.T., Agu, F.I., The shifted Gompertz-G family of distributions: properties and applications, Mathematica Slovaca, 71(5) (2021), 1291-1308. https://doi.org/10.1515/ms-2021-0053
  • Hamedani, G.G., Rasekhi, M., Najibi, S., Yousof, H.M., Alizadeh, M., Type II general exponential class of distributions, Pakistan Journal of Statistics and Operation Research, 15(2) (2019), 503-523. https://doi.org/10.18187/pjsor.v15i2.1699
  • Handique, L., Ahsan, A.L., Chakraborty, S., Generalized modified exponential-G family of distributions: its properties and applications, International Journal of Mathematics and Statistics, 21(1) (2020), 1-17.
  • Hussein, M., Elsayed, H., Cordeiro, G.M., A new family of continuous distributions: properties and estimation, Symmetry, 14(2) (2022), 276. https://doi.org/10.3390/sym14020276
  • Korkmaz, M.Ç., A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application, Journal of Applied Statistics, 47(12) (2020), 2097-2119. https://doi.org/10.1080/02664763.2019.1704701
  • Lee, E. T., & Wang, J., Statistical Methods for Survival Data Analysis, John Wiley & Sons, 2003.
  • Moakofi, T., Oluyede, B., Gabanakgosi, M., The Topp-Leone odd Burr III-G family of distributions: Model, properties and applications, Statistics, Optimization & Information Computing, 10(1) (2022), 236-262. https://doi.org/10.19139/soic-2310-5070-1135
  • Moakofi, T., Oluyede, B., Chipepa, F., Makubate, B., Odd power generalized Weibull-G family of distributions: Model, properties and applications, Journal of Statistical Modelling: Theory and Applications, 2(1) (2021), 121-142. DOI:10.22034/JSMTA.2021.2333
  • Nascimento, A.D., Silva, K.F., Cordeiro, G.M., Alizadeh, M., Yousof, H.M., Hamedani, G.G., The odd Nadarajah-Haghighi family of distributions: properties and applications, Studia Scientiarum Mathematicarum Hungarica, 56(2) (2019), 185-210. https://doi.org/10.1556/012.2019.56.2.1416
  • Oluyede, B., Chipepa, F., The Marshall-Olkin odd exponential half logistic-G family of distributions: Properties and applications, Statistics, Optimization & Information Computing, 11(2) (2021), 479-503. https://doi.org/10.19139/soic-2310-5070-938
  • Rannona, K., Oluyede, B., Chipepa, F., Makubate, B., The Marshall-Olkin-exponentiated odd exponential half logistic-G family of distributions with applications, Eurasian Bulletin of Mathematics, 4(3) (2022), 134-161.
  • Schwarz, Gideon E., Estimating the dimension of a model, Annals of Statistics, 6(2) (1978), 461–464. https://www.jstor.org/stable/2958889
  • Teamah, A.E.A., Elbanna, A.A., Gemeay, A.M., Heavy-tailed log-logistic distribution: Properties, risk measures and applications, Statistics, Optimization & Information Computing, 9(4) (2021), 910-941. https://doi.org/10.19139/soic-2310-5070-1220
  • Zhao, W., Khosa, S.K., Ahmad, Z., Aslam, M., Afify, A.Z., Type-I heavy-tailed family with applications in medicine, engineering and insurance, PloS One, 15(8) (2020). https://doi.org/10.1371/journal.pone.0237462
  • Zhao, J., Ahmad, Z., Mahmoudi, E., Hafez, E.H., Mohie El-Din, M.M., A new class of heavytailed distributions: Modeling and simulating actuarial measures, Complexity, 2021 (2021), https://doi.org/10.1155/2021/5580228
There are 31 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Research Articles
Authors

Thatayaone Moakofi 0000-0002-2676-7694

Broderick Oluyede 0000-0002-9945-2255

Publication Date December 29, 2023
Submission Date October 26, 2022
Acceptance Date August 7, 2023
Published in Issue Year 2023 Volume: 72 Issue: 4

Cite

APA Moakofi, T., & Oluyede, B. (2023). The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(4), 921-958. https://doi.org/10.31801/cfsuasmas.1195058
AMA Moakofi T, Oluyede B. The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2023;72(4):921-958. doi:10.31801/cfsuasmas.1195058
Chicago Moakofi, Thatayaone, and Broderick Oluyede. “The Type I Heavy-Tailed Odd Power Generalized Weibull-G Family of Distributions With Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 4 (December 2023): 921-58. https://doi.org/10.31801/cfsuasmas.1195058.
EndNote Moakofi T, Oluyede B (December 1, 2023) The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 4 921–958.
IEEE T. Moakofi and B. Oluyede, “The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 4, pp. 921–958, 2023, doi: 10.31801/cfsuasmas.1195058.
ISNAD Moakofi, Thatayaone - Oluyede, Broderick. “The Type I Heavy-Tailed Odd Power Generalized Weibull-G Family of Distributions With Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/4 (December 2023), 921-958. https://doi.org/10.31801/cfsuasmas.1195058.
JAMA Moakofi T, Oluyede B. The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:921–958.
MLA Moakofi, Thatayaone and Broderick Oluyede. “The Type I Heavy-Tailed Odd Power Generalized Weibull-G Family of Distributions With Applications”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 4, 2023, pp. 921-58, doi:10.31801/cfsuasmas.1195058.
Vancouver Moakofi T, Oluyede B. The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(4):921-58.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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