scholarly journals Erratum: Note of correction: “Laplace approximations to posterior moments and marginal distributions on circles, spheres, and cylinders”

2012 ◽  
Vol 40 (4) ◽  
pp. 770-771
Author(s):  
Parthasarathy Bagchi ◽  
Joseph B. Kadane
Keyword(s):  
Marginal Distributions ◽  
Posterior Moments

scholarly journals Copulaesque Versions of the Skew-Normal and Skew-Student Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 815
Author(s):  
Christopher Adcock
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Degrees Of Freedom ◽  
Special Functions ◽  
Normal Distribution Function ◽  
Skew Normal Distribution ◽  
Marginal Distributions ◽  
Student’S T ◽  
Normal Copula ◽  
Skew Normal

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples.

scholarly journals Priors for Macroeconomic Time Series and Their Application

1994 ◽  
Vol 10 (3-4) ◽  
pp. 609-632 ◽  
Author(s):  
John Geweke
Keyword(s):  
Time Series ◽  
Prior Distribution ◽  
Odds Ratio ◽  
General Trend ◽  
Stationary Model ◽  
Posterior Odds ◽  
Posterior Odds Ratio ◽  
The Family ◽  
Macroeconomic Time Series ◽  
Posterior Moments

This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student-t disturbances. The model is linear in the data, but nonlinear in parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter that can be readily elicited. The main technical contribution is the construction of posterior moments, densities, and odd ratios by using a six-step Gibbs sampler. Mappings from the index parameter of the family of prior distribution to posterior moments, densities, and odds ratios are developed for several of the Nelson–Plosser time series. These mappings show that the posterior distribution is not even approximately Gaussian, and they indicate the sensitivity of the posterior odds ratio in favor of difference stationarity to the choice of the prior distribution.

ON THE EXTREMAL DEPENDENCE COEFFICIENTS OF GAUSSIAN DISTRIBUTIONS

Vestnik NSUEM ◽  
2021 ◽  
pp. 161-167
Author(s):  
S. E. Khrushchev
Keyword(s):  
Close Correlation ◽  
Gaussian Copula ◽  
Marginal Distributions ◽  
Gaussian Distributions ◽  
Extremal Dependence ◽  
Zero Values ◽  
Coronavirus Infection ◽  
The Russian Federation ◽  
The One ◽  
The Relationship

The paper considers a way to represent the relationship between indicators in the form of copulas. Copulas are popular mathematical tools. This is due to the fact that, on the one hand, the marginal distributions of indicators are divided in the copulas, and on the other hand, the structure of the relationship between these marginal distributions is divided, which makes it  possible to very effectively study the connections that arise in real  populations. Special attention in the work is paid to extremal dependence coefficients - important numerical characteristics of the connection in conditions of extreme small or extremely large values of indicators. It is shown that even under conditions of close correlation between the indices for a two-dimensional Gaussian distribution, the lower and upper coefficients of the extreme dependence take zero values. This indicates the impossibility of predicting the values of one indicator when fixing too small or too large values of another indicator. This work shows that the relationship between the number of COVID-19 coronavirus infections per 100,000 people and the number of deaths from COVID-19 coronavirus infection per 100,000 people in the regions of the Russian Federation can be represented in the form of a Gaussian copula.

scholarly journals Interpolation of groundwater quality parameters with some values below the detection limit

2011 ◽  
Vol 15 (9) ◽  
pp. 2763-2775 ◽  
Author(s):  
A. Bárdossy
Keyword(s):  
Detection Limit ◽  
Maximum Likelihood ◽  
Groundwater Quality ◽  
Likelihood Estimation ◽  
Quality Parameters ◽  
Indicator Kriging ◽  
West Germany ◽  
Marginal Distributions ◽  
Copula Models ◽  
Measuring Device

Abstract. For many environmental variables, measurements cannot deliver exact observation values as their concentration is below the sensitivity of the measuring device (detection limit). These observations provide useful information but cannot be treated in the same manner as the other measurements. In this paper a methodology for the spatial interpolation of these values is described. The method is based on spatial copulas. Here two copula models – the Gaussian and a non-Gaussian v-copula are used. First a mixed maximum likelihood approach is used to estimate the marginal distributions of the parameters. After removal of the marginal distributions the next step is the maximum likelihood estimation of the parameters of the spatial dependence including taking those values below the detection limit into account. Interpolation using copulas yields full conditional distributions for the unobserved sites and can be used to estimate confidence intervals, and provides a good basis for spatial simulation. The methodology is demonstrated on three different groundwater quality parameters, i.e. arsenic, chloride and deethylatrazin, measured at more than 2000 locations in South-West Germany. The chloride values are artificially censored at different levels in order to evaluate the procedures on a complete dataset by progressive decimation. Interpolation results are evaluated using a cross validation approach. The method is compared with ordinary kriging and indicator kriging. The uncertainty measures of the different approaches are also compared.

scholarly journals Nonparametric Estimation of Multivariate Extreme Value Copulas with Known and Unknown Marginal Distributions

2021 ◽  
Vol 2068 (1) ◽  
pp. 012003
Author(s):  
Ayari Samia ◽  
Mohamed Boutahar
Keyword(s):  
Distribution Function ◽  
Empirical Distribution Function ◽  
Extreme Values ◽  
Empirical Distribution ◽  
Extreme Value ◽  
Dependence Function ◽  
Marginal Distributions ◽  
Nonparametric Estimators ◽  
Monte Carlo Experiments ◽  
Multivariate Extreme Values

Abstract The purpose of this paper is estimating the dependence function of multivariate extreme values copulas. Different nonparametric estimators are developed in the literature assuming that marginal distributions are known. However, this assumption is unrealistic in practice. To overcome the drawbacks of these estimators, we substituted the extreme value marginal distribution by the empirical distribution function. Monte Carlo experiments are carried out to compare the performance of the Pickands, Deheuvels, Hall-Tajvidi, Zhang and Gudendorf-Segers estimators. Empirical results showed that the empirical distribution function improved the estimators’ performance for different sample sizes.

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