Abstract
Using data from 39 well-distributed and long-record stations over the area, we found gamma distribution to be the most suitable probability model from among the Pearsonian models that show good fit to monthly rainfall in the Asian summer monsoon. We show that the monthly rainfall distribution is not Gaussian and the simple square-root, cube-root, and logarithmic transformations are of limited utility for normalizing the rainfall distribution.
A Craig type chart indicates that the rainfall distribution is a Type I distribution or a special or limiting case of this distribution; these distributions are fitted to monthly rainfall, and the goodness-of-fit is tested by the chi-square test. The gamma distribution (Pearson's Type III), which is a limiting case of Type I distribution and next, to the Gaussian distribution in simplicity, gives a good fit to monthly rainfall at all the stations in each of the summer monsoon months; the Kolmogorov-Smirnov test and the variance ratio test confirm this good fit. The Type I distribution shows good fit to June rainfall at 26 stations, July rainfall at 31 stations, August rainfall at 24 stations, and September rainfall at 23 stations. Type IX, a special case of Type I, shows good fit to June rainfall at four stations, July rainfall at two stations, August rainfall at four stations, and September rainfall at three stations.
In cases where the gamma and other Pearsonian distributions show good fit, the gamma distribution is found to be the most suitable. The spatial distribution of the scale and shape parameters of the gamma distribution applied to monthly rainfall over the area is examined and the chief features of the distribution are indicated and explained. Deciles of the mixed gamma distribution applied to monthly rainfall are tabulated; these can be used to obtain the monthly rainfall probabilities required by any user.
