Probability Distribution Rate Analysis

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PROBABILITY DISTRIBUTION FUNCTIONS IN RAINFALL ANALYSIS Sugandh Pratap Singh (2016CEW2427)
INTRODUCTION
Water is the source of all life on Earth. The total amount of water present on the earth is fixed and does not change. Rainfall intensities of various frequencies and durations are the basic input in hydrologic design. Precipitation frequency analysis is used to estimate rainfall depth at a point for a specified exceedence probability and duration. Rainfall frequency analysis is usually based on annual maximum series at a site (at-site analysis) or from several sites (regional analysis).
The maximum value may not always yield the true maximum amount for a specified duration. For
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(1993) indicated that all rainfall stations at the same area cannot be described by just a single probability distribution, assuming these stations belong to a certain probability distribution and form a cluster. All the stations in the same area can be classified into several clusters in accordance with their probability distributions.
PDFs AND GOODNESS OF FIT TESTS
A probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey etc. A probability distribution can either be univariate or multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution (a joint probability distribution) gives the probabilities of a random vector (a set of two or more random variables) taking on various combinations of values. Important and commonly encountered univariate probability distributions include the binomial distribution, the hyper geometric distribution, and the normal distribution. The multivariate normal distribution is a commonly encountered multivariate
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• For annual rainfall predictions, the log Pearson type III was found to be the best fit PDF as suggested by the results of the three of the goodness of fit tests viz. chi square test, NSE and RE.

• The average weekly rainfall data showed that 26th week has experienced the highest rainfall of about 229 mm and the minimum rainfall of 3.3 mm was received during the 33rd week.

• The weekly values indicated that out of 52 weeks, 42 weeks have received rainfall of more than 21 mm (considering the crop water demand of 3 mm per day) whereas the remaining 10 weeks have received less than 21 mm of rainfall.

• Weekly rainfall pattern over the 5-year interval showed that the onset of the monsoon was usually in the 2nd standard week (June 8) and withdrawal was in the 30th week (December 27).

• The monthly rainfall data analyses indicated that the month of July has received the maximum rainfall of 547.4 mm followed by the month of June which has received the second highest rainfall of 543.4 mm.

• The month of December has received the lowest rainfall of 18

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