Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 42, 2013 - Issue 13
Submit an article Journal homepage
1,042
Views
43
CrossRef citations to date
0
Altmetric
Original Articles

The Bivariate Normal Copula

Christian Meyer DZ BANK AG, Frankfurt, GermanyCorrespondence[email protected]
Pages 2402-2422 | Received 23 Apr 2010, Accepted 29 Jul 2011, Published online: 14 May 2013
 
Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days

Abstract

We collect well-known and less-known facts about the bivariate normal distribution and translate them into copula language. In addition, we provide various (equivalent) expressions for the bivariate normal copula, we compute its Gini's gamma, and we derive improved bounds and approximations on its diagonal.

Mathematics Subject Classification:

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related Research Data

Probability Integrals of Multivariate Normal and Multivariate $t^1$
Source: The Institute of Mathematical Statistics
Copula Methods in Finance: Cherubini/Copula
Source: John Wiley
Approximations to the probability integral and certain percentage points of a multivariate analogue of Student's t-distribution*
Source: Oxford University Press (OUP)
A comparison of bivariate normal algorithms
Source: Informa UK Limited
A Simple Approximation for Bivariate and Trivariate Normal Integrals
Source: JSTOR
Numerical computation of rectangular bivariate and trivariate normal and t probabilities
Source: Springer Science and Business Media LLC
Comparison of algorithms for bivariate normal probability over a rectangle based on self-validated results from interval analysis ∗
Source: Informa UK Limited
Distributions Generated by Perturbation of Symmetry
Source: Wiley
Bibliography on the Multivariate Normal Integrals and Related Topics
Source: Institute of Mathematical Statistics
A REDUCTION FORMULA FOR NORMAL MULTIVARIATE INTEGRALS
Source: JSTOR
Speed and accuracy comparison of bivariate normal distribution approximations for option pricing
Source: Infopro Digital Services Limited
Fast and Accurate Calculation of Owen's T Function
Source: Foundation for Open Access Statistics
Ueber die Entwicklung einer Function von beliebig vielen Variablen nach Laplaceschen Functionen höherer Ordnung.
Source: Zenodo
The bivariate normal integral
Source: Oxford University Press (OUP)
Algorithm AS 76: An Integral Useful in Calculating Non-Central t and Bivariate Normal Probabilities
Source: JSTOR
Mills' ratio: Monotonicity patterns and functional inequalities
Source: Elsevier BV
A Simple Approximation for Bivariate Normal Probabilities
Source: Informa UK Limited
Estimation of inter-sector asset correlations
Source: Infopro Digital Services Ltd
Determining Distribution for the Quotients of Dependent and Independent Random Variables by Using Copulas
Source: Basel: MDPI
A note on multivariate Gaussian estimates
Source: Elsevier BV
A series expansion for the bivariate normal integral
Source: Infopro Digital Services Limited
Bayes estimation subject to uncertainty about parameter constraints
Source: Oxford University Press (OUP)
Ordinal Measures of Association
Source: Informa UK Limited
On the computation of the bivariate normal integral
Source: Informa UK Limited
A note on the equicorrelated multivariate normal distribution
Source: JSTOR
Calculation of Univariate and Bivariate Normal Probability Functions
Source: The Institute of Mathematical Statistics
Bounds on the Bivariate Normal Distribution Function
Source: Informa UK Limited
New Bivariate Pareto Type II Models.
Source: MDPI AG
Mathematical Contributions to the Theory of Evolution. XI. On the Influence of Natural Selection on the Variability and Correlation of Organs
Source: The Royal Society
THE PROBABILITY INTEGRAL FOR TWO VARIABLES
Source: Oxford University Press (OUP)
Computation of the bivariate normal integral
Source: American Mathematical Society (AMS)
Tables for Computing Bivariate Normal Probabilities
Source: Institute of Mathematical Statistics
Symmetric Multivariate and Related Distributions
Source: Chapman and Hall/CRC
A Simple Approximation to the Bivariate Normal Distribution with Large Correlation Coefficient
Source: Academic Press.
Mathematical Contributions to the Theory of Evolution. VII. On the Correlation of Characters not Quantitatively Measurable
Source: The Royal Society
MULTIVARIATE EXTREMES, AGGREGATION AND DEPENDENCE IN ELLIPTICAL DISTRIBUTIONS
Source: Cambridge University Press (CUP)
Models and Applications
Source: John Wiley & Sons, Inc.

Linking provided by 

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.