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