(a) Probability Distribution of Peak flow
The probability distribution of the peak flow was derived from the data on the yearly
maximum of average daily discharges in cusecs. These are given in Table 8 below. (The
reader who is not familiar with the mathematics used can safely skip the section which
derives the probability distribution.)
Table 8
Peak Flows at Rhondia, 1935- 52
(thousand cusecs)
Year Maximum of average daily
discharges
1935 422.5
1936 174.5
1937 121.7
1938 61.9
1939 258.5
1940 266.5
1941 625.0
1942 375.0
1943 251.3
1944 153.5
1945 120.9
1946 313.7
1947 259.6
1948 229.7
1949 230.1
1950 245.9
1951 347.4
1952 168.3The statistical theory of extreme values, as developed by Gumbel [2] and others, was
applied to derive the probability distribution of the peak flow. The logic of the theory
can be described briefly as follows. Consider a sample containing n independent
observations on a continuous variate x. We seek the probability distribution of the
maximum value of x in the sample. Clearly, the probability distribution of x and on the
sample size. Thus, let f(x) be the probability distribution of x and let (x) be the
probability that the value x is the largest among n independent observations.
Then φn(x) = {F(x)}n
Where F (x) = ƒx- 8 f(x) dx is the cumulative probability distribution of x