Employing Artificial Intelligence Algorithms to Estimate the Hazard Function of the Inverse Gompertz Distribution with a Practical Application
DOI:
https://doi.org/10.47134/ppm.v2i4.2053Keywords:
Inverse Gompertz Distribution, Properties, Maximum Likelihood Method, Genetic Algorithm, Risk FunctionAbstract
Environmental pollution is one of the most important and serious problems facing humanity today, due to its direct impact on the health of humans and other living organisms. In recent years, an increase in environmental pollution rates has been observed, significantly impacting human health and leading to the emergence of numerous diseases, such as cancer, pneumonia, poisoning, birth defects, and others. Given the importance and seriousness of the issue and its direct impact on human life, this research was conducted to determine the percentage of pollution caused by two of the most important factors in air pollution, CO2. This research was conducted based on the explanatory variables: average temperature, average dew point, average humidity, average wind speed, and the average amount of crude oil used in the refining process. In this research, the risk function of the inverse Gompertz model was estimated using artificial intelligence algorithms, namely the genetic algorithm. These methods were applied to air pollution data obtained from the Central Refineries Company in Baghdad (Dora Refinery), which represents daily measurements of environmental pollution compounds based on time for the period from 2019 to 2025.
References
Adepoju KA, Chukwu AU, Wang M. The beta power exponential distribution. J Stat Sci Appl. 2014;2:37–46. DOI: https://doi.org/10.17265/2328-224X/2014.01.004
Ahmad A, Ahmad SP, Ahmed A. Transmuted inverse Rayleigh distribution: a generalization of the inverse Rayleigh distribution. Math Theory Model. 2014;4(7).
Alizadeh M, Afify AZ, Eliwa MS, Ali S. The odd log-logistic Lindley-G family of distributions: properties, Bayesian and non-Bayesian estimation with applications. Comput Stat. 2019. doi:10.1007/s00180-019-00932-9. DOI: https://doi.org/10.1007/s00180-019-00932-9
Basheer AM. Alpha power inverse Weibull distribution with reliability application. J Taibah Univ Sci. 2019;13(1):423–432. DOI: https://doi.org/10.1080/16583655.2019.1588488
Cordeiro GM, Cristino CT, Hashimoto EM, Ortega EM.The beta generalized Rayleigh distribution. Stat Pap. 2013;54:133–161. DOI: https://doi.org/10.1007/s00362-011-0415-0
E. Demir , Ö. Akkus , " An Introductory Study on How the Genetic Algorithm Works in the Parameter Estimation of Binary Logit Model", IJS:BAR, pp.162-180 , 2015.
Elbatal I, Elgarhy M. Statistical properties of Kumaraswamy quasi Lindley distribution. Int J Math Trends Technol. 2013;4:237–246.
El-Gohary A, El-Bassiouny AH, El-Morshedy M. Inverse flexible Weibull extension distribution. Int J Comput Appl. 2015;115:46–51. DOI: https://doi.org/10.5120/20127-2211
Eliwa MS, El-Morshedy M, Afify AZ. The odd Chen generator of distributions: properties and estimation methods with applications in medicine and engineering. J Natl Sci Found Sri Lanka. 2019. To appear. DOI: https://doi.org/10.4038/jnsfsr.v48i2.8790
Eliwa MS, El-Morshedy M. Bivariate Gumbel-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with application. Ann Data Sci. 2018. doi:10.1007/s40745-018-00190-4. DOI: https://doi.org/10.1007/s40745-018-00190-4
Eliwa MS, El-Morshedy M. Discrete flexible distribution for over-dispersed data: statistical and reliability properties with estimation approaches and applications. J Appl Stat. 2020b. To appear.
El-Morshedy M, El-Bassiouny AH, El-Gohary A. Exponentiated inverse flexible Weibull extension distribution. J Stat Appl Prob. 2017;6(1):169–183. DOI: https://doi.org/10.18576/jsap/060114
El-Morshedy M, Eliwa MS, El-Gohary A, Khalil AA. Bivariate exponentiated discrete Weibull distribution: statisticalproperties, estimation, simulation and applications. Math Sci. 2019b. doi:10.1007/s40096-019-00313-9 DOI: https://doi.org/10.1007/s40096-019-00313-9
El-Morshedy M, Eliwa MS, Nagy H. A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications. J Appl Stat. 2019a. doi:10.1080/02664763.2019.1638893. DOI: https://doi.org/10.1080/02664763.2019.1638893
El-Morshedy M, Eliwa MS. The odd flexible Weibull-H family of distributions: properties and estimation with applications to complete and upper record data. Filomat. 2019;33(9). To appear. DOI: https://doi.org/10.2298/FIL1909635E
Ghitany ME, Al-Mutairi DK, Balakrishnan N, Al-Enezi LJ.Power Lindley distribution and associated inference.Comput Stat Data Anal. 2013;64:20–33. DOI: https://doi.org/10.1016/j.csda.2013.02.026
Haq MA. Kumaraswamy exponentiated inverse Rayleigh distribution. Math Theory Model. 2016;6(3):93–104. DOI: https://doi.org/10.2991/jsta.2016.15.3.8
I. Yousef ,"Some methods for estimating the conditional logistic regression model in the case of longitudinal data and their application in environmental pollution " A master’s thesis in statistics submitted to the College of Administration and Economics at the University of Baghdad , 2017.
Kundu D, Raqab MZ. Generalized Rayleigh distribution different methods of estimation Comput Stat Data Anal. 2005;49:187–200. DOI: https://doi.org/10.1016/j.csda.2004.05.008
M.S. Ahmed , "Forecasting of Environmental Pollution Using Box-Genghis Models for Al-Waziriya Station" Research Diploma in Statistics presented to the College of Administration and Economics at the University of Baghdad , 2015.
Merovci F, Elbatal I. Weibull-Rayleigh distribution: theory and applications. Appl Math Inf Sci. 2015;9(4):2127–2137.
Merovci F. Transmuted exponentiated exponential distribution.Math Sci Appl E-Notes. 2013a;1(2):112–122.
Merovci F. Transmuted Rayleigh distribution. Austrian J Stat. 2013c;42(1):21–31. DOI: https://doi.org/10.17713/ajs.v42i1.163
Oguntunde PE, Adejumo AO. Transmuted inverse exponential distribution. Int J Adv Stat Prob. 2015;3(1):1–7. DOI: https://doi.org/10.14419/ijasp.v3i1.3684
Oguntunde PE, Babatunde OS, Ogunmola AO. Theoretical analysis of the Kumaraswamy inverse exponential distribution. Int J Stat Appl. 2014;4(2):113–116.
R. Alshenawy (2020) A new one parameter distribution: properties and estimation with applications to complete and type II censored data, Journal of Taibah University for Science, 14:1, 11-18, DOI: 10.1080/16583655.2019.1698276 DOI: https://doi.org/10.1080/16583655.2019.1698276
S.A Al-Rudaini, "The use of the genetic algorithm in estimating the parameters of the binary logistic regression model with practical application" A master’s thesis in statistics submitted to the College of Administration and Economics at the University of Baghdad ,2019
S.Sefian , M. Benbouziane ,"Portfolio Selection Using Genetic Algorithm" , MPRA , pp. 1-12 , 2012.
Sarhan M, Lotfi T, Hamilton DC. A new lifetime distribution and its power transformation. J Probab Stat. 2014. article ID 532024. DOI: https://doi.org/10.1155/2014/532024




