Probability Distribution of Annual Droughts

by Eratakulan S. Joseph, (A.M.ASCE), Dept. of Mathematics, Keystone Jr. Coll., La Plume, PA,

Serial Information: Journal of the Irrigation and Drainage Division, 1970, Vol. 96, Issue 4, Pg. 461-474

Document Type: Journal Paper


The object herein is to establish a suitable probability distribution for annual droughts of 14-day periods. The approach used was to fit certain theoretical distributions to the observed data and to select, by suitable criteria, the distribution which best described the data. The relative adequacy of five distributions was studied. They were the gamma, the log-normal, the square root normal, the normal and the Grumbel's extreme value (Weibull) distributions. Two techniques were used to determine the goodness-of-fit: (1) the chi-squared test; and (2) a comparison of the skewness-kurtosis relation. Tests were performed using the data of 37 stations in the Missouri River Basin whose annual droughts in succeeding years were found to be randomly distributed with respect to time. The results of either test reveals that the gamma distribution is the first choice, the Weibull being next, and the log-normal comes in third.

Subject Headings: Probability | Probability distribution | Droughts | Gamma function | Vegetation | Comparative studies | Skewness | Hydrologic data | Missouri River

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