A Note on the Bivariate Chi Distribution

Krishnaiah, P. R.; Hagis, Peter; Steinberg, Leon

doi:10.1137/1005034

Cited by 61 publications

(25 citation statements)

References 2 publications

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“…Evaluating v,(T) and using Ferguson [4], the LMPI test statistic T~ can be written as Although the above integrals can be evaluated (Krishnaiah, Hagis and Steinberg [6]), the resulting expressions involve infinite sums unless both n~-4-n2-3 and n~-2 are even integers. We consider below this special case, assuming n~--2=2r and n~+n~-3=2s.…”

Section: A Locally Optimum Test When P Is Knownmentioning

confidence: 99%

Some tests with unbalanced data from a bivariate normal population

Sarkar¹,

Sinha²,

Krishnaiah³

1983

Ann Inst Stat Math

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Section: A Locally Optimum Test When P Is Knownmentioning

confidence: 99%

Some tests with unbalanced data from a bivariate normal population

Sarkar¹,

Sinha²,

Krishnaiah³

1983

Ann Inst Stat Math

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“…while (ynsl, yn82) follows a bivariate chi distribution with f dJ., [5,6]. Making f d.f., and correlation coefficient (c.c.…”

Section: The Probability Density Function Of (Ti T~)mentioning

confidence: 99%

Series Representations of a Bivariate Singly Noncentral t-Distribution

Krishnan

1972

Journal of the American Statistical Association

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“…[15][16][17][18][19][20]). Only very recently, Hagedorn et al have derived corresponding results for 3 × 3 complex central Wishart matrices [21].…”

Section: Introductionmentioning

confidence: 99%

Diagonal distribution of a complex non-central Wishart matrix: A new trivariate non-central chi-squared density

Dharmawansa

McKay

2009

Journal of Multivariate Analysis

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a b s t r a c tThis paper derives the joint density of a particular trivariate non-central χ 2 distribution corresponding to the diagonal elements of a 3 × 3 complex non-central Wishart matrix.This distribution is important for a number of practical statistical signal processing applications, including synthetic aperture radar, extra-solar planet detection, and multiantenna wireless communications. The density expression is in the form of an infinite series representation which converges rapidly and is easy to compute. The joint density of the diagonal elements of a 2 × 2 complex non-central Wishart matrix is also derived by simple reduction of the trivariate result.

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A Note on the Bivariate Chi Distribution

Cited by 61 publications

References 2 publications

Some tests with unbalanced data from a bivariate normal population

Some tests with unbalanced data from a bivariate normal population

Series Representations of a Bivariate Singly Noncentral t-Distribution

Diagonal distribution of a complex non-central Wishart matrix: A new trivariate non-central chi-squared density

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