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Trabajos de Estadistica

, Volume 2, Issue 2, pp 41–53 | Cite as

Affinity between complex distribution functions

  • Antonio Dorival Campos
Article
  • 7 Downloads

Summary

By analogy to the real case established by Matusita (1955) we introduce the concept of affinity between two complex distribution function. We also establish a concrete expression for the affinity between two complexk-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 realk-variate normal distributions.

Key words

affinity complex distribution function distance k-dimensional complex normal distribution complex inner product complex conjugate Hermitian matrix 

A.M.S. classification

primary 62E99 secondary 62H20 

Afinidad entre funciones de distribución complejas

Resumen

Por analogía con caso real establecido por Matusita (1955), introducimos el concepto de afinidad entre dos funciones de distribución complejas. Establecemos también una expresión explícita para la afinidad entre dos distribuciones normales complejask-dimensionales cuando las matrices de covarianzas poseen una forma especial. Generalizaciones de estos resultados son presentadas y las expresiones aquí obtenidas son comparadas con las de Matusita (1966, 1967) relativas a la afinidad entre distribuciones normales realesk-dimensionales.

Palabras clave

afinidad función de distribución compleja distancia distribución normal complejak-dimensional producto interno complejo complejo conjugado matriz hermítica 

Clasificación A.M.S.

primaria 62E99 secundaria 62H20 

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References

  1. GOODMAN, N. R. (1963): «Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction)»,Ann. Math. Statist., 34, 152–177.MATHCrossRefMathSciNetGoogle Scholar
  2. JOHNSON, N. L., and KOTZ, S (1972):Distributions in Statistics: Continuous Multivariate Distributions, John Wiley & Sons, Inc.Google Scholar
  3. MATUSITA, K. (1955): «Decision rules based on the distance for problems of fit, two samples and estimation»,Ann. Math. Statist., 26, 631–640.MATHCrossRefMathSciNetGoogle Scholar
  4. — (1966): «A distance and related statistics in multivariate analysis»,Multivariate Analysis (P. R. Krishnaiah, ed.), Academic Press, New York, 187–200.Google Scholar
  5. — (1967): «On the notion of affinity of several distributions and some of its applications»,Ann. Inst. Statist. Math., 19, 181–192.MATHCrossRefMathSciNetGoogle Scholar
  6. WOODING, R. A. (1956): «The multivariate distribution of comlex normal variables»,Biometrika 43, 212–215.MATHMathSciNetGoogle Scholar

Copyright information

© Springer 1987

Authors and Affiliations

  • Antonio Dorival Campos
    • 1
  1. 1.Dep. de Mat. Apl. ã Biologia Faculdade de Medicina de Ribeirâo PretoUniversidade de Sâo PauloRibeirâo PretoBrasil

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