Üst Rekor Değerleri Kullanılarak Porsuk Barajındaki Su Seviyesinin Tahmini

Calısmanın temel amacı ust rekor değerleri yardımıyla belirli cevresel konuların nasıl analiz edileceğini gostermektir. Bu calısmada, Eskisehir iline su sağlayan Porsuk Barajı icin 1974 Ocak - 2005 Aralık donemine ait aylara iliskin ortalama gunluk su miktarıi verileri ust rekor değerleri yardımıyla analiz edilmistir. Devlet Su Đsleri (DSI) 3. Bolge Mudurluğu’nden elde edilen veriler kullanıarak, baraja gelen ortalama gunluk su miktarlarıı ust rekor değrleri uc dağıı (Normal, Logistic, Rayleigh) yardııla tahmin edilmistir. Analiz sonucunda Mart, Nisan, Mayı ve Haziran aylarıda barajdaki su seviyesinin oldukca fazla olduğ belirlenmistir. Bu nedenle bu aylarda baraja tahmin edilen miktarlarda su gelmesi halinde barajda kontrolsuz su bıakımasıgibi onemli sorunlar olabilecektir.

Anahtar Kelimeler:

Önkestirim, Porsuk Barajı, Üst Rekor Değerleri

Estimation Of Water Level In Porsuk Dam By Using Upper Record Values

The main purpose of this study is to show how upper record statistics help in analyzing certain environmental issues. In this study, we analyzed the average daily water amount data from the monthly data of the Porsuk dam which supplies water for Eskisehir between the time period of January 1974 and December 2005 by using upper record values. By using this data taken from State Hydraulic Works (SHW) 3rd Regional Directorate, the upper record values of daily average amounts of coming water to the dam are estimated via three probability distributions: Normal, Logistic and Rayleigh. As a result, it has been realized that the water amount in the dam is very much in March, April, May and June. For this reason, if the estimated amount of water comes to the dam, there could be considerable problems, such as uncontrolled water set free for the dam.

Keywords:

Prediction, Porsuk Dam, Upper Record Values.,

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[1] K.N. Chandler, “The Distribution and Frequency of Record Values”, J.R.Statistic.Soc.B., 14,1952.
[2] F.G. Foster and A. Stuart, “Distribution Free Tests in Time-Series Bond on the Breaking of Records”, J.Roy.Stat. Soc.Series B, 16, 1954.
[3] F.G. Foster and D. Teichroew, “A Sampling Experiment on the Powers of the Records Tests for Trend in a Time Series” , J.Royal Stat.Soc. Series B, 17 ,1955.
[4] M.F. Neuts, “Waiting times between record observations”, J. Applied Probability, 30, pp. 147-159, 1967.
[5] P.T. Holmes and W. Strawderman, “A note on the waiting times between record observations”, J. Applied Probability, 6, pp. 711-714, 1969.
[6] R.W. Shorrock, “On record values and record times”, J.App.Prob., 9, pp. 316-326, 1972.
[7] S.I. Resnick, “Limit laws for record values”, Stoch. Proc. Appl., 1, pp. 67-82, 1973.
[8] R.W. Shorrock, “Record values and inter-record times”, J.App.Prob., 10, pp. 543-555, 1973.
[9] H.N. Nagaraja, “On a characterization based on record values”, Austral J.Stat., 19, pp. 70- 73, 1977.
[10] M. Ahsanullah, “Characterization of the exponential distribution by record values”, Sankhyá, Series B, 41, pp. 116-121, 1979.
[11] P. Deheuvels, “The characterization of distributions by order statistics and record values- a unified approach”, J.App. Prob., 21, pp. 326-334, 1984.
[12] N. Glick, “Breaking records and breaking boards”, The Amer. Math. Mont., 85, pp. 2-26, 1978.
[13] H. N. Nagaraja, “On the expected values of record values”, Austral J. Stat., 20(2), pp. 176-182, 1978.
[14] V.B. Nevzorov, “Records”, Theory Prob. App., 32, pp. 201-228, 1988.
[15] M. Ahsanullah, “Record Statistics”, Nova Science Pub., New York, 1995.
[16] B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, “Records”, John Wiley and Sons Inc, New York, 1998.
[17] M. Ahsanullah, “Linear prediction of record values for the two parameter exponential distribution”, Ann. Inst. Statist. Math., 32, pp. 363-368, 1980.
[18] I.R. Dunsmore, “The future occurrence of records”, Annals of the Institue of Statistical Mathematics, 35, pp. 267-277, 1983.
[19] H.N. Nagaraja, “Record values and extreme value distributions”, J. Appl. Probab., 19, pp. 233-239, 1982.
[20] H.N. Nagaraja, “Asymptotic linear prediction of extreme order statistics”, Ann. Inst. Statist. Math., 36, pp. 289-299, 1984.
[21] M. Ahsanullah, “Estimation of the parameters of the Gumbel distribution based on the m record values”, Comput. Statist. Quart., 3, pp. 231-239, 1990.
[22] N. Balakrishnan, M. Ahsanullah and P.S. Chan, “On the logistic record values and associated inference”, J. Appl. Statist. Sci., 2 (3), pp. 233-248, 1995.
[23] N. Balakrishnan and P.S. Chan, “Record values from Rayleigh and Weibull distributions and associated inference”, Extreme Value Theory and Applications, 3, pp. 41-51, 1993.
[24] N. Balakrishnan and P.S. Chan, “On the Normal record values and associated inference”, Statistics and Prob. Letters, 39, pp. 73-80, 1998.
[25] M.Z. Raqab, “Inferences for generalized exponential distribution based on record statistics”, Journal of Statistical Planning and Inference, 104, pp. 339–350, 2002.
[26] R.E. Benestad, “Record-values, nonstationarity tests and extreme value distributions”, Global and Planetary Change, 44, pp. 11 –26, 2004.
[27] M.Z. Raqab, “Nonparametric prediction intervals for future rainfall records”, Environmetrics, 17 (5), pp. 457 – 464, 2005.
[28] P.S. Chan, “A statistical study of log-gamma distribution”, Ph.D. Dissertation, McMaster University, Canada, 1993.
[29] N. Balakrishnan and A.C. Cohen, “Order Statistics and Inference: Estimation Methods”, Academic Press, San Diego, 1991.
[30] K. Koçak, ve L. Saylan, “Trakya’da Yağıs Rejimindeki Değisi min Fraktal Analiz ile Belirlenmesi”, III. Atmosfer Bilimleri Sempozyumu, 2003, Đstanbul, Bildiri kitabı, ss. 354- 361.