By analogy to the real case established by Matusita (1955) we introduce the concept of affinity between two complex distribution functions. We also establish a concrete expression for the affinity between two complex k-variate normal distributions when the covariance matrices assume a special form. Generalizations of these results are presented and the expressions here obtained are compared with those obtained by Matusita (1966, 1967) relative to the affinity between real k-variate normal distributions
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