scholarly journals Truncation Mixture R-Vine Copulas

2021 ◽  
Author(s):  
Fadhah Alanazi
Keyword(s):  
Simulation Study ◽  
Real Data ◽  
Computational Time ◽  
Model Parameters ◽  
Copula Models ◽  
Truncation Level ◽  
Truncation Method ◽  
Tree Estimation ◽  
Vine Copula ◽  
Vine Copulas

Uncovering hidden mixture correlation among variables have been investigating in the literature using mixture R-vine copula models. These models are hierarchical in nature. They provides a huge flexibility for modelling multivariate data. As the dimensions increases, the number of the model parameters that need to be estimated is increased dramatically, which becomes along with huge computational times and efforts. This situation becomes even much more harder and complicated in the mixture Regular vine models. Incorporating truncation method with mixture Regular vine models will reduce the computation difficulty for the mixture based models. In this paper, tree-by-tree estimation mixture model is joined with the truncation method, in order to reduce the computational time and the number of the parameters that need to be estimated in the mixture vine copula models. A simulation study and a real data applications illustrated the performance of the method. In addition, the real data applications show the affect of the mixture components on the truncation level.

scholarly journals Sequential Truncation of R-Vine Copula Mixture Model for High-Dimensional Datasets

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Fadhah Amer Alanazi
Keyword(s):  
Mixture Model ◽  
Real Data ◽  
Computational Time ◽  
Model Parameters ◽  
Copula Models ◽  
Truncation Level ◽  
Truncation Method ◽  
Tree Estimation ◽  
Vine Copula ◽  
High Dimensional Datasets

Uncovering hidden mixture dependencies among variables has been investigated in the literature using mixture R-vine copula models. They provide considerable flexibility for modeling multivariate data. As the dimensions increase, the number of the model parameters that need to be estimated is increased dramatically, which comes along with massive computational times and efforts. This situation becomes even much more complex and complicated in the regular vine copula mixture models. Incorporating the truncation method with a mixture of regular vine models will reduce the computation difficulty for the mixture-based models. In this paper, the tree-by-tree estimation mixture model is joined with the truncation method to reduce computational time and the number of parameters that need to be estimated in the mixture vine copula models. A simulation study and real data applications illustrated the performance of the method. In addition, the real data applications show the effect of the mixture components on the truncation level.

scholarly journals Nonparametric estimation of simplified vine copula models: comparison of methods

2017 ◽  
Vol 5 (1) ◽  
pp. 99-120 ◽  
Author(s):  
Thomas Nagler ◽  
Christian Schellhase ◽  
Claudia Czado
Keyword(s):  
Nonparametric Estimation ◽  
Tail Dependence ◽  
Real Data ◽  
Parametric Models ◽  
Copula Models ◽  
Data Application ◽  
Models Comparison ◽  
Vine Copula ◽  
Bivariate Copula ◽  
Vine Copulas

AbstractIn the last decade, simplified vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities and bivariate copula densities. Besides parametric models, several approaches to nonparametric estimation of vine copulas have been proposed. In this article, we extend these approaches and compare them in an extensive simulation study and a real data application. We identify several factors driving the relative performance of the estimators. The most important one is the strength of dependence. No method was found to be uniformly better than all others. Overall, the kernel estimators performed best, but do worse than penalized B-spline estimators when there is weak dependence and no tail dependence.

scholarly journals Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1786 ◽  
Author(s):  
A. M. Abd El-Raheem ◽  
M. H. Abu-Moussa ◽  
Marwa M. Mohie El-Din ◽  
E. H. Hafez
Keyword(s):  
Simulation Study ◽  
Stress Test ◽  
Real Data ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Model Parameters ◽  
Data Set ◽  
Accelerated Life

In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

scholarly journals A Cognitive Diagnosis Model for Identifying Coexisting Skills and Misconceptions

2017 ◽  
Vol 42 (3) ◽  
pp. 179-191 ◽  
Author(s):  
Bor-Chen Kuo ◽  
Chun-Hua Chen ◽  
Jimmy de la Torre
Keyword(s):  
Simulation Study ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Cognitive Diagnosis ◽  
Future Research ◽  
Model Parameters ◽  
Cognitive Diagnosis Models ◽  
Proposed Model ◽  
Diagnosis Model

At present, most existing cognitive diagnosis models (CDMs) are designed to either identify the presence and absence of skills or misconceptions, but not both. This article proposes a CDM that can be used to simultaneously identify what skills and misconceptions students possess. In addition, it proposes the use of the expectation-maximization algorithm to estimate the model parameters. A simulation study is conducted to evaluate the viability of the proposed model and algorithm. Real data are analyzed to demonstrate the applicability of the proposed model, and compare it with existing CDMs. Furthermore, a real data–based simulation study is conducted to determine how the correct classification rates in the context of the proposed model can be improved. Issues related to the proposed model and future research are discussed.

scholarly journals Explaining predictive models using Shapley values and non-parametric vine copulas

2021 ◽  
Vol 9 (1) ◽  
pp. 62-81
Author(s):  
Kjersti Aas ◽  
Thomas Nagler ◽  
Martin Jullum ◽  
Anders Løland
Keyword(s):  
Traditional Approach ◽  
Simulated Data ◽  
Real Data ◽  
Data Sets ◽  
Data Set ◽  
Wide Range ◽  
Shapley Values ◽  
Non Gaussian ◽  
Vine Copula ◽  
Vine Copulas

Abstract In this paper the goal is to explain predictions from complex machine learning models. One method that has become very popular during the last few years is Shapley values. The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence, there have recently been attempts of appropriately modelling/estimating the dependence between the features. Although the previously proposed methods clearly outperform the traditional approach assuming independence, they have their weaknesses. In this paper we propose two new approaches for modelling the dependence between the features. Both approaches are based on vine copulas, which are flexible tools for modelling multivariate non-Gaussian distributions able to characterise a wide range of complex dependencies. The performance of the proposed methods is evaluated on simulated data sets and a real data set. The experiments demonstrate that the vine copula approaches give more accurate approximations to the true Shapley values than their competitors.

scholarly journals A new generalization of Aradhana distribution: Properties and applications

2020 ◽  
Vol 16 (2) ◽  
pp. 51-66
Author(s):  
A. Hassan ◽  
S. A. Dar ◽  
P. B. Ahmad ◽  
B. A. Para
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Real Data ◽  
Statistical Properties ◽  
Model Parameters ◽  
R Software ◽  
Data Set

AbstractIn this paper, we introduce a new generalization of Aradhana distribution called as Weighted Aradhana Distribution (WID). The statistical properties of this distribution are derived and the model parameters are estimated by maximum likelihood estimation. Simulation study of ML estimates of the parameters is carried out in R software. Finally, an application to real data set is presented to examine the significance of newly introduced model.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

scholarly journals Stochastic Modeling of Hydroclimatic Processes Using Vine Copulas

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2156
Author(s):  
George Pouliasis ◽  
Gina Alexandra Torres-Alves ◽  
Oswaldo Morales-Napoles
Keyword(s):  
Time Series ◽  
Stochastic Modeling ◽  
Copula Models ◽  
Multiple Processes ◽  
Spatial Dependencies ◽  
Probabilistic Dependence ◽  
Temporal And Spatial ◽  
Vine Copula ◽  
Synthetic Time Series ◽  
Hydroclimatic Variables

The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is, alternating dry and wet intervals), and spatial and temporal dependencies that pose a particular challenge to their study. Vine copula models offer an appealing approach to generate synthetic time series because of their ability to preserve any marginal distribution while modeling a variety of probabilistic dependence structures. In this work, we focus on the stochastic modeling of hydroclimatic processes using vine copula models. We provide an approach to model intermittency by coupling Markov chains with vine copula models. Our approach preserves first-order auto- and cross-dependencies (correlation). Moreover, we present a novel framework that is able to model multiple processes simultaneously. This method is based on the coupling of temporal and spatial dependence models through repetitive sampling. The result is a parsimonious and flexible method that can adequately account for temporal and spatial dependencies. Our method is illustrated within the context of a recent reliability assessment of a historical hydraulic structure in central Mexico. Our results show that by ignoring important characteristics of probabilistic dependence that are well captured by our approach, the reliability of the structure could be severely underestimated.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

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