EXPECTED VALUES OF COSTS AND REVENUES DEPENDENT ON DROUGHT

In earlier papers on drought, sequences of wet and dry months were treated as realisations of binomial trials with periodic probabilities of failure (dry months), and the cost-revenue outcomes of alternative drought strategies were handled probabilistically. When costs and revenues may be represented by a set of second degree polynomials over a set of adjacent subranges of the time scale, their expectation may be expressed as a simple closed formula in the twelve probabilities of dry months. As an illustration of the use of these new formulae, means and standard deviations of drought duration calculated in this manner are presented for three typical localities in Queensland. Previously known closed formulae for the mean and the variance in the case where all calendar months have equal probability of being dry emerge as special cases and are verified.