03151nam a2200421 4500 20260818170528.0 140198 th eng .b10476957 AIT Thesis no. 857 Huynh, Ngoc Phien On the mean range of partial sums in the case of independent gamma variables Bangkok : Asian Institute of Technology, 1976 65 p. Thesis ; no. 857 A thesis submitted in partial fulfillment of the requirement for the Degree of Master of Science at the Asian Institute of Technology, Bangkok, Thailand. Thesis (M.Sc.) - Asian Institute of Technology, 1976 Under the assumption that the reservoir is of infinite capacity, the mean or expected value of the storage required to maintain the long term mean inflow is investigated when the annual inflow is distributed as independent gamma variable. This is done by introducing the range of partial sums of the fluctuations of the inflow around its mean. The inflow is first standardized, and by means of the data generation method, an approximate equation of the mean range is then obtained. It is expressed in terms of Cs, the skewness coefficient of the inflow distribution, and of n, the number of years, in the following form: 10' E (R ) 1. 65 n = I 3_ exp (- 0.0475Cs ) O.7(n-l)0.6+ 2 n E i-1/2 i=l In the case when n=l, this expression approximates well the exact formula which is derived mathematically: E(R1) = 2/a [l( /a , a-1)- I (-a - ,a) /ci+1 in which a is the shape parameter of the gamma distribution, and I(u,p) is the incomplete gamma function. The mean storage required for regulating the mean inflow is then obtained by multiplying E(Rn ) by the standard deviation of the inflow discharges. Reservoirs Arbhabhirama Anat, Chairperson Prathet Sutabutr, Co-Chairperson Okamoto, Masami, Examination Committee Selvalingam, Selvadore, Examination Committee The British Council, Scholarship Donor Asian Institute of Technology. Thesis ; no. 857 Full-Text http://203.159.5.9/ait-thesis/detail.php?q=B23673 .b10476957 mnait x 260310 2 951012 m a x 0 mnait mnait mnarc 20 40 Barcode : 30050002837309 CREATED : 1995-10-15 RECORD # : i10597219 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 Barcode : 30050003037172 CREATED : 1995-10-15 RECORD # : i10597220 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 Barcode : 30050160091640 CREATED : 2016-04-27 RECORD # : i12958116 LPATRON : 0 LCHKIN : - # RENEWALS : 0 # OVERDUE : 0 IUSE3 : 0 TOT CHKOUT : 0 TOT RENEW : 0 83015 83015 0 0 0 0 MAIN MAIN mnait 2026-08-18 0 AIT Thesis no. 857 30050002837309 2026-08-18 17:05:28 1 2026-08-18 20 0 0 0 0 MAIN MAIN mnait 2026-08-18 0 AIT Thesis no. 857 30050003037172 2026-08-18 17:05:28 2 2026-08-18 20 0 0 0 0 MAIN MAIN mnarc 2026-08-18 0 AIT Thesis no. 857 30050160091640 2026-08-18 17:05:28 2026-08-18 40