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<br />extensively to allow a similar analysis. The variable used to define dry and wet conditions is the <br /> <br />Standardized Precipitation Index (SPI) which was used in Edwards and McKee (1997). <br /> <br />Precipitation and snow have two qualities that influence how the SPI is calculated. The first is <br /> <br />that it is highly variable in time so that many years are needed to obtain useful estimates of its <br /> <br />probability distribution. The second is that precipitation and snow are not normally distributed <br /> <br />statistically which means that the distribution is skewed and the mean and median are not the <br /> <br />same. Assume as an example that precipitation is observed monthly for many years. All of the <br /> <br />monthly values are used to fit a Gamma frequency distribution which is given by: <br /> <br />-x <br />g(x)= 1 xr-1eP. /3>0 r >0 <br />/3 r rcr) , , <br /> <br />(1) <br /> <br />Thom (1966) has shown the Gamma distribution fits precipitation quite well. The frequency <br /> <br />density g(x) for the Gamma is a two parameter function with /3 and r being the fitted parameters. <br /> <br />The variable x is precipitation. The mean or average value of x is /3 r. The cumulative <br /> <br />probability is given by: <br /> <br />x <br />G(x) = f g(x)dx <br />o <br /> <br />(2) <br /> <br />where G(x) is the probability that x is equal to or less than x. <br /> <br />In the application to drought, precipitation is fitted to the Gamma distribution. Then at a <br /> <br />particular time, precipitation is observed. The observed value (Xi) is used with the Gamma to <br /> <br />determine the cumulative probability at that time, G(x;}. Next an equiprobability transformation <br /> <br />is made from the Gamma function to the normally distributed function with a mean of zero and a <br /> <br />12 <br />