A bivariate beta distribution

Olkin, Ingram; Liu, Ruixue

doi:10.1016/s0167-7152(03)00048-8

Cited by 157 publications

(119 citation statements)

References 1 publication

Supporting

Mentioning

115

Contrasting

Unclassified

Order By: Relevance

“…Table 1 contains many such values. (The very few numerical values of ρ B in common with those given when υ 2 = υ 1 by Jones (2001) and Olkin & Liu (2003) are confirmed in these calculations.) * * * Table 1 about here * * * Table 1 indicates a pattern of dependence of ρ B on n 1 , n 2 , υ 1 and υ 2 which reflects precisely the dependence of ρ F on n 1 , n 2 , υ 1 and υ 2 , obtained analytically and described at the end of Section 2.3.…”

Section: Product Moments and Correlationsupporting

confidence: 70%

“…The univariate marginals of distribution (10) are, of course, each beta distributions with arbitrary parameters {n 1 /2, υ 1 /2} and {n 2 /2, υ 2 /2}, respectively. When υ 2 = υ 1 , (10) reduces to the bivariate beta density in Libby & Novick (1982), Jones (2001) and Olkin & Liu (2003).…”

Section: Densitymentioning

confidence: 99%

“…Graphs of f B 1 ,B 2 when υ 1 = υ 2 are given in Jones (2001, Fig. 4, though the two frames of that figure have had their labelling swopped) and Olkin & Liu (2003, Fig. 1).…”

Section: Densitymentioning

confidence: 99%

“…Jones (2001) applies transformations (3) to both marginal variates F ′ 1 and F ′ 2 of the standard F distribution of (1) (in place of Y in (3)) to obtain bivariate beta and skew t distributions with parameters {n 1 /2, n 3 /2} and {n 2 /2, n 3 /2}, respectively. The bivariate beta distribution was, unfortunately, not acknowledged to be a special case of the multivariate generalized beta distribution proposed by Libby & Novick (1982) and has since also been reinvented by Olkin & Liu (2003). Note, again, the restriction that the second parameter of each marginal distribution be the same.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions

El-Bassiouny

Jones

2008

Stat Methods Appl

View full text Add to dashboard Cite

The classical bivariate F distribution arises from ratios of chi-squared random variables with common denominators. A consequent disadvantage is that its univariate F marginal distributions have one degree of freedom parameter in common. In this paper, we add a further independent chisquared random variable to the denominator of one of the ratios and explore the extended bivariate F distribution, with marginals on arbitrary degrees of freedom, that results. Transformations linking F , beta and skew t distributions are then applied componentwise to produce bivariate beta and skew t distributions which also afford marginal (beta and skew t) distributions with arbitrary parameter values. We explore a variety of properties of these distributions and give an example of a potential application of the bivariate beta distribution in Bayesian analysis.

show abstract

Section: Product Moments and Correlationsupporting

confidence: 70%

Section: Densitymentioning

confidence: 99%

“…Graphs of f B 1 ,B 2 when υ 1 = υ 2 are given in Jones (2001, Fig. 4, though the two frames of that figure have had their labelling swopped) and Olkin & Liu (2003, Fig. 1).…”

Section: Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions

El-Bassiouny

Jones

2008

Stat Methods Appl

View full text Add to dashboard Cite

show abstract

“…28 The gene-biomarker expression values on prostate cancer patients are considered as diagnosis marker for illustration of correlated Beta Bivariate distribution. 27,29,30,32 The proposed method is performed through MCMC technique to discriminate the TLV of gene -biomarker expressions among healthy and diseased individual. The specific Bivariate Beta distributions are studied and finally some empirical applications with gene-biomarker expression data are presented to obtain the TLV.…”

mentioning

confidence: 99%

Detecting Diagnostic Accuracy of Biomarkers Through a Bivariate Beta Distribution

Bhattacharjee¹,

Vishwakarma²,

Thomas³

2017

Turkiye Klinikleri J Biostat

View full text Add to dashboard Cite

An EM‐type approach for classification of bivariate MALDI‐MS data and identification of high fertility markers

et al. 2018

View full text Add to dashboard Cite

Dairy cows are responsible for a fair amount of gas emissions in the atmosphere (mainly methane, ammonia, and carbon dioxide), as well as waste outputs. Therefore, identifying high‐fertility breeding cows and increasing fertility rates can diminish pollution and help minimize the effect of global warming and improve the environmental impact of the farming system. As a step to achieve this goal, changes in the lipid composition of the bovine uterus exposed to greater (LF‐LCL group) or lower (SF‐SCL group) concentrations of progesterone during postovulation were investigated by matrix‐assisted laser desorption ionization mass spectrometry. Two measurements were made for each cow, and after preprocessing the data, the measurements available to analysis consist of relative intensities at significant 76 mass‐to‐charge ratio (m/z) values identifying specific ions in the spectra. Due to the small sample size, seven cows in the LF‐LCL group and 10 cows in the SF‐SCL group, the usual methods could not discriminate between groups. A model‐based approach was therefore proposed, and due to the discrete nature of the data, a truncated mixture of bivariate beta distributions was fitted to the data using an expectation–maximization algorithm. However, unlike the usual approach for mixture density estimation problems, to each 76 m/z value, we assign an unobserved label shared by all cows in the same group. The role of these labels is similar to the frailty effect in survival models in which all cows in a given group would share some random effect due to group effect. These labels will be used to identify m/z values, which could potentially account for different fertility rates.

show abstract

A bivariate beta distribution

Cited by 157 publications

References 1 publication

A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions

A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions

Detecting Diagnostic Accuracy of Biomarkers Through a Bivariate Beta Distribution

An EM‐type approach for classification of bivariate MALDI‐MS data and identification of high fertility markers

Contact Info

Product

Resources

About