zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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 θ. It is a positive definite quadratic differential form based on the elements of the information matrix for θ. 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:
62E99Statistical distribution theory