San José State University
Department of Economics
Thayer Watkins
Silicon Valley
& Tornado Alley

Estimates for the Parameters
of the Lévy Stable Distributions for
Daily Rainfallof the Days With Rain
in San Jose, California (1908-2000)

The δ parameter of the Lévy stable distribution should be the mean value of the distribution if the distribution has a mean value. For α≤1 the distribution does not have a properly defined expected value. The values of δ found for the monthly distributions are not equal to the average rainfall (of those days with rainfall) but they are closely correlated with those monthly average figures as is shown below. The monthly that is out-of-line is September probably because of the problems of fitting the singular storm of 1918 into the distribution. It is notable that August is also moderately out-of-line perhaps reflectly a certain instability of rainfall patterns in the early fall. Given the procedure for finding the values of ν it is a notable that the two measures of average rainfall should be so closely correlated.

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