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PREDICTING FUTURE DATA FROM GAMMA-MIXTURE AND BETA-MIXTURE DISTRIBUTIONS AND APPLICATION TO THE RECOVERY RATE OF COVID-19
Keywords:
mixture distributions, predictive interval, gamma distribution, beta distribution, point predictor, COVID-19.DOI:
https://doi.org/10.17654/0972361723061Abstract
This paper addresses the problem of predicting future order statistics arising from mixture distributions. This study generalizes Barakat et al.’s [1] work that focused only on the data from a mixture of exponential distributions to wide models including the mixture-gamma and beta-mixture distributions. For these two lifetime models, we construct prediction intervals and point predictions for future observations. Two cases are considered, in the first case, we assume a fixed sample size, while in the second case, the sample size is assumed to be a positive integer-valued random variable independent of the observations. A simulation study is carried out for corroborating the finding and illustrative purposes. Finally, a practical application of the proposed method is applied to the recovery rate of COVID-19 data sets.
Received: August 3, 2023
Accepted: September 18, 2023
References
H. M. Barakat, O. M. Khaled and H. A. Ghonem, Predicting future lifetime for mixture exponential distribution, Communications in Statistics: Simulation and Computation 51(7) (2020a), 3533-3552. doi: 10.1080/03610918.2020.1715434.
K. S. Kaminsky and P. I. Nelson, 15 Prediction of Order Statistics, Volume 17, Elsevier, 1998. doi: 10.1016/S0169-7161(98)17017-7.
H. M. Barakat, M. E. El-Adll and A. E. Aly, Exact prediction intervals for future exponential lifetime based on random generalized order statistics, Computers and Mathematics with Applications 61(5) (2011), 1366-1378.
doi: 10.1016/j.camwa.2011.01.002.
H. M. Barakat, M. E. El-Adll and A. E. Aly, Prediction intervals of future observations for a sample of random size from any continuous distribution, Mathematics and Computers in Simulation 97 (2014), 1-13.
doi: 10.1016/j.matcom.2013.06.007.
URL http://dx.doi.org/10.1016/j.matcom.2013.06.007.
H. M. Barakat, O. M. Khaled and H. A. Ghonem, New method for prediction of future order statistics, Quality Technology and Quantitative Management 18(1) (2020b), 101-116.
https://www.tandfonline.com/doi/abs/10. 1080/16843703.2020.1782087.
H. M. Barakat, O. M. Khaled and H. A. Ghonem, Predicting future order statistics with random sample size, AIMS Mathematics 6(5) (2021), 5133-5147.
doi: 10.3934/MATH.2021304.
URL http://www.aimspress.com/article/doi/10.3934/math.2021304.
S. Bhushan, A. Kumar, M. T. Akhtar, S. A. Lone, Shashi Bhushan, Logarithmic type predictive estimators under simple random sampling, AIMS Mathematics 7(7) (2022), 11992-12010. doi: 10.3934/MATH.2022668.
URL http://www.aimspress.com/rticle/doi/10. 3934/math.2022668.
M. Z. Raqab and H. M. Barakat, Prediction intervals for future observations based on samples of random sizes, Journal of Mathematics and Statistics 14(1) (2018), 16-28. doi:10.3844/JMSSP.2018.16.28.
H. M. Barakat, E. M. Nigm, M. E. El-Adll and M. Yusuf, Prediction of future generalized order statistics based on exponential distribution with random sample size, Statistical Papers 59(2) (2018a), 605-631.
doi: 10.1007/S00362-016-0779-2/TABLES/12.
URL https://link.springer.com/article/10.1007/s00362-016-0779-2.
J. F. Lawless, Prediction intervals for the two parameter exponential distribution, Technometrics 19(4) (1977). doi: 10.2307/1267887.
L. Costantini, C. Nwafor, S. Lorenzi, A. Marrano, P. Ruffa, P. Moreno-Sanz, S. Raimondi, A. Schneider, I. Gribaudo and M. S. Grando, Prediction intervals for Weibull order statistics, Statistica Sinica 7(22) (1997), 43.
doi: 10.4/JQUERY-UI.MIN.JS. URL https://works.bepress.com/h{_}hsieh/1/.
B. S. Everitt and D. J. Hand, Finite Mixture Distributions, Springer Netherlands, 1981. doi: 10.1007/978-94-009-5897-5.
A. Feldmann and W. Whitt, Fitting mixtures of exponentials to long-tail distributions to analyze network performance models, Performance Evaluation 31(3-4) (1998), 245-279. doi: 10.1016/S0166-5316(97)00003-5.
Z. F. Jaheen, On record statistics from a mixture of two exponential distributions, Journal of Statistical Computation and Simulation 75(1) (2005), 1-11.
doi: 10.1080/00949650410001646924.
H. M. Barakat, A new method for adding two parameters to a family of distributions with application to the normal and exponential families, Statistical Methods and Applications 24(3) (2015), 359-372.
doi: 10.1007/S10260-014-0265-8.
URL https://ideas.repec.org/a/spr/stmapp/v24y2015i3p359-372.html.
H. M. Barakat, O. M. Khaled and N. K. Rakha, Modern techniques in data analysis, with application to the water pollution, Proceedings of the Latvian Academy of Sciences, Section B: Natural, Exact, and Applied Sciences 72(3) (2018b), 184-192. doi: 10.2478/PROLAS-2018-0005.
H. M. Barakat, A. W. Aboutahoun and N. N. El-Kadar, On some generalized families arising from mixture normal distribution with applications, Communications in Statistics: Simulation and Computation 50(1) (2021), 198-216. doi: 10.1080/03610918.2018.1554110.
B. Long and Z. Jiang, Estimation and prediction for two-parameter Pareto distribution based on progressively double Type-II hybrid censored data, AIMS Mathematics 8(7) (2023), 15332-15351.
doi: 10.3934/MATH.2023784.
URL http://www.aimspress.com/rticle/doi/10.3934/math.2023784.
A. E. Aly, M. E. El-Adll, H. M. Barakat and R. A. Aldallal, A new least squares method for estimation and prediction based on the cumulative hazard function, AIMS Mathematics 8(9) (2023), 21968-21992.
doi: 10.3934/math.20231120.
URL https://www.aimspress.com/article/doi/10.3934/math.20231120.
Y. Wang and D. M. Blei, The blessings of multiple causes, Journal of the American Statistical Association 114(528) (2019), 1574-1596.
doi: 10.1080/01621459.2019.1686987.
URL https://www.tandfonline.com/doi/abs/10. 1080/01621459.2019.1686987.
H. M. Barakat and O. M. Khaled, Toward the establishment of a family of distributions that may fit any dataset, Communications in Statistics: Simulation and Computation 46(8) (2017), 6129-6143.
doi: 10.1080/03610918.2016.1197245.
I. Rahimi, F. Chen and A. H. Gandomi, A review on COVID-19 forecasting models, Neural Computing and Applications (2021), 1-11.
doi: 10.1007/S00521-020-05626-8/TABLES/3.
URL https://link.springer.com/article/10.1007/s00521-020-05626-8.
A. S. Ahmar and E. B. del Val, SutteARIMA: Short-term forecasting method, a case: Covid-19 and stock market in Spain, Science of the Total Environment 729 (2020), 138883. doi: 10.1016/J.SCITOTENV.2020.138883.
B. A. Smith, A novel IDEA: The impact of serial interval on a modified-Incidence Decay and Exponential Adjustment (m-IDEA) model for projections of daily COVID-19 cases, Infectious Disease Modelling 5 (2020), 346-356.
doi: 10.1016/J.IDM.2020.05.003.
H. Okagbue, M. O. Adamu and T. A. Anake, Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication, Heliyon 6(11) (2020), e05523.
doi: 10.1016/j.heliyon.2020.e05523.
C. Bernard and S. Vanduffel, Quantile of a Mixture, 2014.
doi: 10.48550/arxiv.1411.4824. URL http://arxiv.org/abs/1411.4824.
S. Evert and M. Baroni, zipfR: Word Frequency Distributions in R. 2020. URL http://purl.org/stefan.evert/zipfR/.
H. H. Ahmad, E. M. Almetwally, M. Elgarhy and D. A. Ramadan, On unit exponential Pareto distribution for modeling the recovery rate of covid-19, Processes 11(1) (2023), 232.
doi: 10.3390/PR11010232. URL https://www.mdpi.com/2227-9717/11/1/232.
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