Prediction of the exponential fractional upper record-values

References

[1] Ahsanullah, M.: Record values and the exponential distribution, Ann. Inst. Stat. Math. 30(A) (1978), 429–433.10.1007/BF02480233Search in Google Scholar

[2] Ahsanullah, M.: Linear prediction of record values for the two parameter exponential distribution, Ann. Inst. Stat. Math. 32(3) (1980), 363–368.10.1007/BF02480340Search in Google Scholar

[3] Ahsanullah, M.: Record Values-Theory and Applications, University Press of America, 2004.Search in Google Scholar

[4] Al-Hussaini, E. K.—Ahmad, A. A.: On Bayesian interval prediction of future records, Test 12 (2003), 79–99.10.1007/BF02595812Search in Google Scholar

[5] Aly, A. E.: Prediction intervals of future generalized order statistics based on generalized extreme value distribution, ProbStat Forum 8 (2015), 148–156.Search in Google Scholar

[6] Aly, A. E.: Prediction and reconstruction of future and missing unobservable modified Weibull lifetime based on generalized order statistics, J. Egyptian Math. Soc. 24 (2016), 309–318.10.1016/j.joems.2015.04.002Search in Google Scholar

[7] Aly, A. E.—Barakat, H. M.—El-Adll, M. E.: Prediction intervals of the record-values process, Revstat Stat. J. 17(3) (2019), 401–427.Search in Google Scholar

[8] Arnold, B. C.—Balakrishnan, N.—Nagaraja, H. N. Records, John Wiley & Sons, New York, (1998).10.1002/9781118150412Search in Google Scholar

[9] Balakrishnan, N.—Ahsanullah, M.—Chan, P. S.: On the logistic record values and associated inference, J. Appl. Stat. 2 (1995), 233–248.Search in Google Scholar

[10] Balakrishnan, N.—Davies, K. F.—Keating, J. P.—Mason, R. L.: Pitman closeness of best linear unbiased and invariant predictors for exponential distribution in one- and two-sample situations, Comm. Statist. Theory Methods 41(1) (2012), 1–15.10.1080/03610920903537301Search in Google Scholar

[11] Barakat, H. M.—El-Adll, M. E.—Aly, A. E.: Exact prediction intervals for future exponential lifetime based on random generalized order statistics. Comput. Math. Appl. 61(5) (2011), 1366–1378.10.1016/j.camwa.2011.01.002Search in Google Scholar

[12] Barakat, H. M.—El-Adll, M. E.—Aly, A. E.: Prediction intervals of future observations for a sample of random size from any continuous distribution, Math. Comput. Simulation 97 (2014), 1–13.10.1016/j.matcom.2013.06.007Search in Google Scholar

[13] Barakat, H. M.—Nigm, E. M.—Aldallal, R. A.: Current records and record range with some applications, J. Korean Statist. Soc. 43 (2014), 263–273.10.1016/j.jkss.2013.09.004Search in Google Scholar

[14] Barakat, H. M.—Nigm, E. M.—Aldallal, R. A.: Exact prediction intervals for future current records and record range from any continuous distribution, SORT 38(2) (2014), 251–270.10.1016/j.jkss.2013.09.004Search in Google Scholar

[15] Barakat, H. M.—Khaled, O. M.—Ghonem, H. A.: Prediction for future data from any continuous distribution. PredictionR. CRAN-R. Institute for Statistics and Mathematics, 2018; https://CRAN.R-project.org/package=PredictionR.Search in Google Scholar

[16] Barakat, H. M.—Nigm, E. M.—El-Adll, M. E.—Yusuf, M.: Prediction of future exponential lifetime based on random number of generalized order statistics under a general set-up, Statist. Papers 59(2) (2018), 605–631.10.1007/s00362-016-0779-2Search in Google Scholar

[17] Barakat, H. M.—Abd Elgawad, M. A.: Asymptotic behavior of the record values in a stationary Gaussian sequence with applications, Math. Slovaca 69(3) (2019), 707–720.10.1515/ms-2017-0259Search in Google Scholar

[18] Barakat, H. M.—Harpy, M. H.: Asymptotic behavior of the records of multivariate random sequences in a norm sense, Math. Slovaca 70(6)(2020), 1457–1468.10.1515/ms-2017-0442Search in Google Scholar

[19] Barakat, H. M.—El-Adll, M. E.—Aly, A. E.: Two-sample nonparametric prediction intervals based on random number of generalized order statistics, Comm. Statist. Theory Methods 50(19) (2021), 4571–4586.10.1080/03610926.2020.1719421Search in Google Scholar

[20] Barakat, H. M.—Khaled, O. M.—Ghonem, H. A.: Predicting future lifetime for mixture exponential distribution, Comm. Statist. Simulation Comput. (2020); https://doi.org/10.1080/03610918.2020.1715434.Search in Google Scholar

[21] Barakat, H. M.—Khaled, O. M.—Ghonem, H. A.: New method for prediction of future order statistics, Qual. Technol. Quant. Manag. 18(1) (2021), 101–116.10.1080/16843703.2020.1782087Search in Google Scholar

[22] Basak, P.—Balakrishnan, N.: Maximum likelihood prediction of future record statistic. In: Mathematical and Statistical Methods in Reliability (B. Lindqvist, K. Doksum, eds.), Chap. 11. World Scientific Publishing, Singapore, (2003), 159–175.10.1142/9789812795250_0011Search in Google Scholar

[23] Berred, A. M.: Prediction of record values, Comm. Statist. Theory Methods 27 (1998), 2221–2240.10.1080/03610929808832224Search in Google Scholar

[24] Bieniek, M.—Szynal, D.: On the fractional record values, Probab. Math. Statist. 24(1) (2004), 27–46.Search in Google Scholar

[25] Chandler, K.: The distribution and frequency of record values, J. R. Stat. Soc. Ser. B. Stat. Methodol. (1952), 220–228.10.1111/j.2517-6161.1952.tb00115.xSearch in Google Scholar

[26] Doganakso, N.—Balakrishnan, N.: A useful property of best linear unbiased prediction with applications to life testing, Amer. Statist. 51 (1997), 22–28.10.1080/00031305.1997.10473581Search in Google Scholar

[27] Dunsmore, I. R.: The future occurrence of records, Ann. Inst. Stat. Math. 35 (1983), 267–277.10.1007/BF02480982Search in Google Scholar

[28] Dziubdziela, W.—Kopocinski, B.: Limiting properties of the k-th record value, Appl. Math. 15 (1976), 187–190.10.4064/am-15-2-187-190Search in Google Scholar

[29] El-Adll, M. E.: Predicting future lifetime based on random number of three parameters Weibull distribution, Math. Comput. Simul. 81 (2011), 1842–1854.10.1016/j.matcom.2011.02.003Search in Google Scholar

[30] El-Adll, M. E.—Ateya, S. F.—Rizk, M. M.: Prediction intervals for future lifetime of three parameters Weibull observations based on generalized order statistics, Arab. J. Math. 1(3) (2012), 295–304.10.1007/s40065-012-0004-7Search in Google Scholar

[31] El-Adll, M. E.—Aly, A. E.: Prediction intervals for future observations of Pareto distribution based on generalized order statistics, J. Appl. Stat. Sci. 22(1–2) (2016), 111–125.Search in Google Scholar

[32] El-Adll, M. E.: Inference for the two-parameter exponential distribution with generalized order statistics, Math. Popul. Stud. 28(1) (2021), 1–23.10.1080/08898480.2019.1681187Search in Google Scholar

[33] Geisser, S.: Predictive Inference: An Introduction, Chapman and Hall, London, 1993.10.1007/978-1-4899-4467-2Search in Google Scholar

[34] Gradshteyn I. S.—Ryzhik, I. M.: Table of Integrals, Series, and Products. New York: Academic Press, 2007.Search in Google Scholar

[35] Gulati, S.—Padgett, W. J.: Parametric and Nonparametric Inference from Record-breaking Data, Springer-Verlag, New York, 2003.10.1007/978-0-387-21549-5Search in Google Scholar

[36] Kaminsky, K. S.—Nelson, P. I.: Best linear unbiased prediction of order statistics in location and scale families, J. Amer. Statist. Assoc. 70(349) (1975), 145–150.10.1080/01621459.1975.10480275Search in Google Scholar

[37] Kaminsky, K. S.—Rhodin, L. S.: Maximum likelihood prediction, Ann. Inst. Stat. Math. 37 (1985), 507–517.10.1007/BF02481119Search in Google Scholar

[38] Kaminsky, K. S.—Nelson, P. I.: Prediction of order statistics. In: Handbook of Statistics 17 (N. Balakrishnan, C. R. Rao, eds.), North Holland, Amsterdam, 1998, 431–450.10.1016/S0169-7161(98)17017-7Search in Google Scholar

[39] Keating, J. P.—Mason, R. L.—Sen, P. K.: Pitman’s Measure of Closeness: A Comparison of Statistical Estimators. SIAM, Philadelphia, Society for Industrial and Applied Mathematics, 1993.10.1137/1.9781611971576Search in Google Scholar

[40] Klar, B.: A note on gamma difference distributions, J. Stat. Comput. Simul. 85(18) (2015), 3708–3715.10.1080/00949655.2014.996566Search in Google Scholar

[41] Lalitha, S.—Kumar, N.: Multiple outlier test for upper outliers in an exponential sample, J. Appl. Stat. 39(6) (2012), 1323–1330.10.1080/02664763.2011.645158Search in Google Scholar

[42] Lawless, J. F.: A prediction problem concerning samples from the exponential distribution with applications in life testing, Technometrics 13 (1971), 725–730.10.1080/00401706.1971.10488844Search in Google Scholar

[43] Lee, E. T.—Wang, J. W.: Statistical Methods for Survival Data Analysis, Third Edition, John Wiley & Sons, 2003.10.1002/0471458546Search in Google Scholar

[44] Lingappaiah, G. S.: Prediction in exponential life testing, Canad. J. Statist. 1 (1973), 113–117.10.2307/3314650.oSearch in Google Scholar

[45] Nagaraja, H. N.: Asymptotic linear prediction of extreme order statistics, Ann. Inst. Stat. Math. 36 (1984), 289–299.10.1007/BF02481971Search in Google Scholar

[46] Nagaraja, H. N.: Comparison of estimators and predictors from two-parameter exponential distribution, Sankhya Ser. B 48 (1986), 10–18.Search in Google Scholar

[47] Nagaraja, H. N.: Record values and related statistics a review, Commun. Stat. Theory Methods 17 (1988), 2223–2238.10.1080/03610928808829743Search in Google Scholar

[48] Nagaraja, H. N.: Prediction problems. In: The Exponential Distribution: Theory and Application (N. Balakrishnan, A. P. Basu, eds.), Gordon and Breach, New York, 1995, pp. 139–163.10.1201/9780203756348-9Search in Google Scholar

[49] Nevzorov, V. B. Records: Mathematical Theory. Transl. Math. Monogr., Amer. Math. Soc., Providence, R. I., 2001.Search in Google Scholar

[50] Pitman, E. J. G.—Wishart, J. The “closest” estimates of statistical parameters, Math. Proc. Cambridge Philos. Soc. 33(2) (1937), 212–222.10.1017/S0305004100019563Search in Google Scholar

[51] Raqab, M.—Balakrishnan, N. Prediction intervals for future records, Statist. Probab. Lett. 78(13) (2008), 1955–1963.10.1016/j.spl.2008.01.064Search in Google Scholar

[52] Raqab, Z. M.—Alkhalfan, A. L.—Balakrishnan, N. Pitman comparisons of predictors of censored observations from progressively censored samples for exponential distribution, J. Stat. Comput. Simul. 86(8) (2016), 1539–1558.10.1080/00949655.2015.1071820Search in Google Scholar

[53] Stigler, M. S. Fractional order statistics, with applictations, J. Amer. Statist. Assoc. 72 (1977), 544–550.10.1080/01621459.1977.10480611Search in Google Scholar

[54] Sultan, K. S.—Abd Ellah, A. H. Exact prediction intervals for exponential lifetime based on random sample size, Int. J. Comput. Math. 83(12) (2006), 867–878.10.1080/00207160601117222Search in Google Scholar