The distribution of a generalized diversity index due to Good

Good (1953, 1982) proposed a generalized diversity index which includes as special cases both Shannon's and Simpson's indices. This index can be furth er generalized as described in Baczkowski et al. (1997, 1998). In this pape r the first four moments of this generalized index are derived for both a g eneral species abundance distribution and the case with all species abundan ces equal, the equiprobable case. This allows the skewness and kurtosis of the index to be determined and thus gives information about the distributio n of the index.