, - - - 0.93 14+1
(c) The value that will never be exceeded is the largest value. Thus, there will be no value above it and the cumulative count for this element is 1. The data for flows in the previous table are simply for values obtained from a field survey. To answer the question of what is the value that will never be exceeded, we have to obtain this value from an exhaustive length of record and read the value that is never exceeded on that particular record. Of course, the count for this largest value would be 1, as mentioned.
Now, what has the field data to do with the determination of the largest value? The use of the field data is to develop a probability distribution. The resulting distribution is then assumed to model the probability distribution of all the possible data obtainable from the problem domain. The larger the number of data and the more representative they are, the more accurate this model will be.
Obtaining the largest value means that the amount of data used to obtain the probability distribution model must be infinitely large; and, in this infinitely large amount of data, there is only one value that is equaled or exceeded. This means that the probability of this one value is 1/infinity = 0. From the probability distribution, the peak weekly flow rate can be extrapolated at probability 0. This is done as follows (with x representing the weekly flow rate):
Therefore, x-4020 4-02-20 - 4000
The probability of values equaled or not exceeded is just the reverse of values equaled or exceeded. In the previous example, the values were arranged in descending order. For the case of value equaled or not exceeded, the values are arranged in ascending order.
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