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Rao’s distance measure. (English) Zbl 0534.62012
The paper examines C. R. Rao’s [Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37, 81-91 (1945)] measure of distance between two distributions depending on an identifying parameter $\theta$. It is a positive definite quadratic differential form based on the elements of the information matrix for $\theta$. In geometric terms, it is the length of the shortest curve joining the two parameter points. For the reason of mathematical difficulties in deriving this measure along Rao’s line of reasoning, the paper discusses alternative methods for computation. The methods are applied to standard distributions belonging to exponential families. The dependence of the distance measure on well known variance- stabilizing-transformations for some families is explained. The case of normal distribution (also multivariate) is studied in detail.
Reviewer: R.Schlittgen

##### MSC:
 6.2e+100 Statistical distribution theory