We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.
Random surfaces with boundary have predictable properties.
problem Understanding the statistical properties of random surfaces.
method Generating surfaces by gluing polygons and analyzing their genus and boundary components.
result Genus and boundary components of random surfaces follow a bivariate normal distribution.
A new Heckman selection model uses a bivariate contaminated normal distribution for more accurate data analysis.
problem Sample selection biases in econometric data analysis.
method Introduces a Heckman selection model using a bivariate contaminated normal distribution and presents an efficient ECM algorithm for parameter estimation.
result The proposed model outperforms normal and Student's t counterparts in real data analysis and simulation studies.
The paper calculates European option prices under a generalized skew normal distribution.
problem European option pricing under a generalized skew normal distribution.
method Proved existence of martingale measure, derived explicit option pricing formula, applied numerical methods.
result Explicit expressions for European option prices are derived.
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We derive also the information geometry of the 3-manifold of McKay bivariate gamma dist…
Study classifies mappings of bivariate normal densities, revealing three types with distinct geometric and statistical properties.
problem Understanding the properties of two-component bivariate normal mixtures.
method Classification via A-equivalence and statistical analysis. result Three distinct types of mappings with specific geometric and statistical properties, and upper bounds for the number of modes.
PCA minor projection is most sensitive to distributional changes in bivariate data.
problem Detecting sparse distributional changes in high-dimensional data.
method Proved that the minor projection of PCA-rotated data is most sensitive to distributional changes defined by Hellinger distance.
result The minor projection is the most sensitive to sparse distributional changes in high-dimensional data.
Modeling stock returns and volatility using a bivariate gamma generalized Laplace law.
problem Analyzing stock returns and volatility using a new statistical model.
method Maximum likelihood estimation for a bivariate generalized Laplace distribution, simplifying to linear regression.
result Explicit estimators derived with nonstandard convergence rates for certain parameter configurations.
SkewD robustly discovers causal relationships in skewed noise models.
problem Distinguishing cause from effect in skewed noise models.
method SkewD extends normal-distribution framework to skew-normal setting for reliable inference.
result SkewD remains robust under high skewness, improving reliability.
Develops a new bivariate process for energy markets with improved simulation methods.
problem Modelling energy markets with stochastic delays and efficient simulations.
method Introduces a novel bivariate Normal Inverse Gaussian process and a path simulation scheme.
result Improves simulation efficiency for energy market models.
Paper simplifies data carving inference with a parametric distribution.
problem Valid inference after selection with data carving.
method Developed a parametric distribution for data carving inference.
result Exact inference for data carving can be computed trivially.
A new CoVaR framework integrates expert views using entropy pooling.
problem Risk assessment and spillover effects from diverse expert views.
method Entropy pooling method to integrate expert views and compute general CoVaR.
result General CoVaR shows linear relationships with expectations and differences in expectations, and nonlinear dependencies with variance, quantiles, and correlation.
GPDFlow models extreme threshold exceedance with flexible dependence using normalizing flows.
problem Challenges in modeling multivariate threshold exceedance probabilities due to infinite parametrizations.
method GPDFlow uses normalizing flows to flexibly represent dependence without explicit parametric assumptions.
result GPDFlow significantly improves modeling accuracy and flexibility compared to traditional parametric methods.
Constructs bivariate quantiles using vine copulas for multivariate analysis.
problem Need for research in multivariate quantiles, especially for bivariate responses.
method Constructs bivariate (conditional) quantiles using vine copula based bivariate regression model with a novel tree sequence graph structure.
result Avoids typical shortfalls of regression like transformations, interactions, collinearity, and quantile crossings.
Method estimates joint distribution of bivariate outcomes.
problem Modeling dependence between bivariate outcomes.
method Semiparametric distribution regression.
result Method performs similarly or better than alternatives in finite samples.
Proposes a new LSTM gate structure using bivariate Beta distribution.
problem Inflexibility of sigmoid gates in modeling multi-modality and skewness, and lack of modeling correlation between gates.
method Introduces a bivariate Beta distribution gate structure within LSTM cells.
result Empirically shows higher gradient values and improved model performance.
Gradient-based methods can be biased by distributional asymmetries in bivariate categorical data.
problem Gradient-based causal discovery methods can be biased by distributional asymmetries in bivariate categorical data.
method Identified and examined two distributional biases: Marginal Distribution Asymmetry and Marginal Distribution Shift Asymmetry. Employed two simple models to demonstrate and control these biases.
result Gradient-based methods can be biased by distributional asymmetries, and these biases can be controlled.
Proposes bivariate DeepKriging for efficient wind field prediction.
problem Challenges in predicting large-scale bivariate wind fields with high spatial variability and heterogeneity.
method Spatially dependent deep neural network (DNN) with embedding layer using spatial radial basis functions.
result Outperforms traditional cokriging predictors and reduces computation time.
New neural networks learn distribution functions using quantiles and moments.
problem Approximating functions of distributions in probability spaces.
method Quantile and moment neural networks, mixing quantile and moment features.
result Moment neural network outperforms others for bivariate distributions.
A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce. These copulas, that include as special cases the Generalized Marshall-Olkin copul…
Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected shortfall when the univariate marginals are known exactly and additional expert inf…
The Bivariate Dynamic Contagion Processes (BDCP) are a broad class of bivariate point processes characterized by the intensities as a general class of piecewise deterministic Markov processes. The BDCP describes a rich dynamic structure where the system is under the influence of both external and internal factors model…
The study evaluates financial risk using copulas and statistical tests.
problem Validating bivariate forecasts in risk evaluation.
method Using copulas to characterize dependencies, applying statistical tests to validate forecasts, removing heteroskedasticity.
result A Student copula accurately describes financial time series dependencies.
New method distinguishes cause from effect using causal velocity.
problem Inferring causal direction from bivariate data.
method Parametrization of bivariate SCMs in terms of causal velocity, using tools from measure transport.
result Method extends beyond known model classes and requires no assumptions on noise distributions.
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process f…
We revisit the Kolmogorov-Smirnov and Cramér-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the "effective" number of independent observations. The generalised GoF tests are not…
New methods optimize sums of bivariate functions on finite domains.
problem Optimizing functions with multiple arguments that are sums of bivariate functions.
method Measure-valued extensions, ℓ2-approximation, entropy-regularization, linear programming, coordinate ascent. result Tractable problem formulations solvable with various methods.
Proposes a sparse linear classifier for classification with pairwise dependencies.
problem Classification accuracy is limited by tree-structured graphical models.
method Semi-parametric approach using sparse linear combination of univariate and bivariate log-transformed densities.
result SLB classifier is competitive with popular methods.
The paper introduces a new model to correct bias in treatment effect estimates due to sample selection.
problem Bias in treatment effect estimates due to sample selection.
method Type 2 Tobit Bayesian Additive Regression Trees (TOBART-2) with Dirichlet Process Mixture distribution and soft trees.
result Corrects bias in treatment effect estimates by accounting for nonlinearities and model uncertainty.
We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong additivity properties. In the case of cobordisms between manifolds with boundary, we pr…
This paper is dedicated to the consistency of systemic risk measures with respect to stochastic dependence. It compares two alternative notions of Conditional Value-at-Risk (CoVaR) available in the current literature. These notions are both based on the conditional distribution of a random variable Y given a stress eve…
The modelling of empirically observed data is commonly done using mixtures of probability distributions. In order to model angular data, directional probability distributions such as the bivariate von Mises (BVM) is typically used. The critical task involved in mixture modelling is to determine the optimal number of co…
New method improves bivariate causal discovery by accurately estimating cause variable complexity.
problem Improper estimation of cause variable complexity in current MDL-based methods.
method Rate-distortion MDL (RDMDL) using information dimension for cause variable complexity estimation.
result RDMDL achieves competitive performance on Tübingen dataset.
MLE and CVE are equivalent under exponential families, leading to faster and more stable EM algorithms.
problem Finding maximum likelihood estimators (MLE) efficiently and stably.
method Proved equivalence between MLE and CVE under exponential families, leading to an EM algorithm.
result EM algorithm achieves the same asymptotic variance as MLE and is faster and more stable.
Levy copulas are the most general concept to capture jump dependence in multivariate Levy processes. They translate the intuition and many features of the copula concept into a time series setting. A challenge faced by both, distributional and Levy copulas, is to find flexible but still applicable models for higher dim…
Study uses a bivariate model to price crude oil futures.
problem Pricing crude oil futures using latent factors and state-space models.
method Modelled short and long term factors as OU processes, estimated using Kalman Filter and maximised Gaussian likelihood.
result Successfully estimated model parameters and factors from WTI Crude Oil NYMEX futures data.
Enhances U-statistics for semi-supervised datasets using unlabeled data.
problem Efficiently utilizing unlabeled data in semi-supervised settings.
method Semi-supervised U-statistics enhanced by unlabeled data.
result Proposed method is asymptotically Normal and more efficient than classical U-statistics.
Paper introduces a new model for cyber insurance pricing.
problem Inaccurate pricing of cyber insurance due to multiple, contagious losses.
method Developed a bivariate compound dynamic contagion process.
result Analytical expressions for the compound process and its moments.
This study examines how noise levels affect causal discovery methods.
problem Impact of noise levels on causal discovery methods.
method Empirical study using Regression with Subsequent Independence Test and Identification using Conditional Variances on ANMs with varying noise levels.
result Causal discovery methods can fail for certain noise levels.
We study the dependence structure of market states by estimating empirical pairwise copulas of daily stock returns. We consider both original returns, which exhibit time-varying trends and volatilities, as well as locally normalized ones, where the non-stationarity has been removed. The empirical pairwise copula for ea…
In this paper we consider a family of Dirac-type operators on fibration P→B equivariant with respect to an action of an etale groupoid. Such a family defines an element in the bivariant K theory. We compute the action of the bivariant Chern character of this element on the image of Connes' map Φ in the cyclic…
DRCD identifies causal direction between continuous and discrete variables using density ratio monotonicity.
problem Inferring causal direction between continuous and discrete variables from observational data.
method Density Ratio-based Causal Discovery (DRCD) method.
result DRCD identifies causal direction between continuous and discrete variables using density ratio monotonicity.
Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, i…
The paper develops deep learning models for personalized treatment rules in survival analysis.
problem Deriving optimal treatment rules for bivariate survival outcomes in randomized trials.
method Adaptive prediction-powered learning using deep neural networks and stochastic policies.
result Maximizes joint survival probability beyond fixed time points (t1,t2). Study on merging predictors in causal and anticausal directions using CMAXENT.
problem Comparing merging predictors in causal and anticausal directions.
method Using CMAXENT as inductive bias, study differences in merging predictors.
result CMAXENT solution reduces to logistic regression in causal direction and LDA in anticausal direction.
New method improves speed of estimating bivariate functional data.
problem Estimating bivariate functional data at faster rates.
method Adapting to directional regularity of bivariate processes.
result Faster rates of convergence achieved through change-of-basis.
A scalable and regularized approach to minimize negative transfer in multivariate Gaussian processes.
problem Challenges in constructing multivariate Gaussian processes, especially with a large number of outputs.
method Regularized pairwise modeling approach using bivariate Gaussian processes.
result Minimizes negative transfer of knowledge between uncorrelated outputs in large multivariate models.
The paper defines new Schur-constant models for non-negative variables.
problem Modeling equilibrium distributions for non-negative variables.
method Introduces Schur-constant equilibrium distribution models for arithmetic non-negative random variables.
result Derived properties include implicit correlation and sum distribution.