Total positivity properties of the bivariate diagonal natural exponential families

DOI10.1016/0167-7152(94)00261-4zbMath0843.62059OpenAlexW1982173578MaRDI QIDQ1914292

Donald St. P. Richards, I-Li Lu

Publication date: 5 June 1996

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(94)00261-4

zbMATH Keywords

orthogonal polynomialsPoisson distributionnormal distributionHermite polynomialsLaguerre polynomialsgamma distributionMeixner polynomialsmultinomial distributionCharlier polynomialsnegative multinomial distributionMehler's formulatotal positivity propertiesbivariate diagonal NEF classesdiagonal natural exponential familiesMehler kernelsvariation-diminishing properties

Mathematics Subject Classification ID

Characterization and structure theory for multivariate probability distributions; copulas (62H05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (2)

Natural Exponential Families and Generalized Hypergeometric Measures ⋮ Some properties of random stationary sequences with bivariate densities having diagonal expansions and nonparametric estimators based on them^*

Cites Work

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• Total positivity, spherical series, and hypergeometric functions of matrix argument
• Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions
• Classes of orderings of measures and related correlation inequalities. II. Multivariate reverse rule distributions
• The diagonal multivariate natural exponential families and their classification

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