The droughts are analyzed by the third asymptotic distribution of smallest values which contains a shape parameter λ, a location parameter θ and a lower limit, the minimum drought ε. If ε = 0 the two remaining parameters are estimated from the sample mean [xbar] and the standard deviation s. If the minimum drought ε is positive it is postulated that the estimate should be smaller than the smallest observed drought x 1. An estimate for λ is obtained from the quotient ([xbar] −x 1)/s. The estimation for θ and ε become linear functions of the mean [xbar] and the smallest drought x 1. Since this theory gives an excellent fit to the observations it can safely be used for forecasting.
No takes yet. Share an insight, caveat, or question.
E. J. Gumbel (1963) studied this question.