COMPOSITE BERNSTEIN COPULAS

2015 ◽  
Vol 45 (2) ◽  
pp. 445-475 ◽  
Author(s):  
Jingping Yang ◽  
Zhijin Chen ◽  
Fang Wang ◽  
Ruodu Wang
Keyword(s):  
Prior Information ◽  
Estimation Method ◽  
Tail Dependence ◽  
Estimation Procedure ◽  
Copula Function ◽  
Simulation Studies ◽  
Copula Functions ◽  
New Class ◽  
Copula Estimation ◽  
Dependency Structures

AbstractCopula function has been widely used in insurance and finance for modeling inter-dependency between risks. Inspired by the Bernstein copula put forward by Sancetta and Satchell (2004, Econometric Theory, 20, 535–562), we introduce a new class of multivariate copulas, the composite Bernstein copula, generated from a composition of two copulas. This new class of copula functions is able to capture tail dependence, and it has a reproduction property for the three important dependency structures: comonotonicity, countermonotonicity and independence. We introduce an estimation procedure based on the empirical composite Bernstein copula which incorporates both prior information and data into the estimation. Simulation studies and an empirical study on financial data illustrate the advantages of the empirical composite Bernstein copula estimation method, especially in capturing tail dependence.

scholarly journals Modelling High Dimensional Paddy Production Data using Copulas

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Nuranisyha Mohd Roslan ◽  
Wendy Ling Shinyie ◽  
Sim Siew Ling
Keyword(s):  
Time Series ◽  
Marginal Distribution ◽  
Reference Group ◽  
Estimation Method ◽  
Information Criterion ◽  
Copula Function ◽  
Archimedean Copula ◽  
Copula Functions ◽  
Estimation Errors ◽  
Elliptical Copula

As the climate change is likely to be adversely affecting the yield of paddy production, thence it has brought a limelight of the probable challenges on human particularly regional food security issues. This paper aims to fit multivariate time series of paddy production variables using copula functions and predicts the next year event based on the data of five countries in southeast Asia. In particular, the most appropriate marginal distribution for each univariate time series was first identified using maximum likelihood parameter estimation method. Next, we performed multivariate copula fitting using two types of copula families, namely, elliptical copula family and Archimedean copula family. Elliptical copula family studied are normal and t copula, while Archimedean copula family considered are Joe, Clayton and Gumbel copulas. The performance of marginal distribution and copula fitting was examined using Akaike information criterion (AIC) values. Finally, we used the best fitted copula model to forecast the succeeding event. In order to assess the performance of copula function, we computed the forecast means and estimation errors of copula function with a generalized autoregressive conditional heteroskedasticity model as reference group. Based on the smallest AIC, the majority of the data favoured the Gumbel copula, which belongs to Archimedean copula family as well as extreme value copula family. Likewise, applying the historical data to forecast the future trends may assist all relevant stakeholders, for instance government, NGO agencies, and professional practitioners in making informed decisions without compromising the environmental as well as economical sustainability in the region.

Research on Function Reliability of Gear Door Lock System With Correlated Failure Models Based on Mixed Copula

2016 ◽  
Author(s):  
Linjie Shen ◽  
Yugang Zhang ◽  
Xinchen Zhuang
Keyword(s):  
Failure Modes ◽  
Tail Dependence ◽  
Copula Function ◽  
Large Error ◽  
Copula Model ◽  
Copula Functions ◽  
Copula Theory ◽  
Reliability Models ◽  
Dynamic Simulation Model ◽  
Door Lock

The gear door lock system (GDLS) is a mechanism with multi-failure modes. It often leads to a large error when ignoring the correlation between failure modes. Copula theory in this work is applied to research the correlation between two failure modes. A dynamic simulation model is constructed to acquire the joint statistics characteristics of the two failure modes. Gumbel and Clayton Copula functions are chosen to establish the reliability model respectively, which shows that the single Copula model cannot fully capture the tail dependence. To solve the problem, a mixed Copula function is constructed. The minimum squared Euclidean distance is adopted to estimate the parameters of the reliability models. It shows that the result of mixed Copula model is the closest to that of the Monte Carlo simulation, and it presents the relative error is at least 46% lower than the single Copula.

scholarly journals Modeling Monotonic Effects of Ordinal Predictors in Bayesian Regression Models

2018 ◽  
Author(s):  
Paul - Christian Bürkner ◽  
Emmanuel Charpentier
Keyword(s):  
Regression Models ◽  
Prior Information ◽  
Estimation Method ◽  
Predictive Performance ◽  
R Package ◽  
Bayesian Regression ◽  
Simulation Studies ◽  
Interaction Terms ◽  
Fully Bayesian ◽  
Ordinal Predictors

Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under- or overestimating the contained information. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modeling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter $b$ representing the direction and size of the effect and a simplex parameter $\zeta$ modeling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may not only be applied to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies, we show that the model is well calibrated and, in case of monotonicity, has similar or even better predictive performance than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects, which allows to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.

scholarly journals Transmuted esscher transformed laplace distribution and its application to microarray analysis

2021 ◽  
Vol 54 (2) ◽  
pp. 167-181
Author(s):  
Punathumparambath Bindu
Keyword(s):  
Likelihood Estimation ◽  
Estimation Procedure ◽  
R Package ◽  
Laplace Distribution ◽  
Simulation Studies ◽  
Microarray Gene Expression ◽  
New Class ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed ◽  
Parameter Values

Esscher transformed Laplace distribution is a new class of asymmetric heavy tailed distribution. In this article, we generalize the Esscher transformed Laplace distribution using the quadratic rank transmutation map to develop transmuted Esscher transformed Laplace distribution. We derived the probability density function of transmuted Esscher transformed Laplace distribution and its various properties were studied. The maximum likelihood estimation procedure is employed to estimate the parameters of the proposed distribution and an algorithm in R package is developed to carry out the estimation. Simulation studies for various choices of parameter values were performed to validate the algorithm. Finally, we fitted the transmuted Esscher transformed Laplace, Esscher transformed Laplace and Gaussian distributions to microarray gene expression dataset and compared them.

scholarly journals An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1815
Author(s):  
Diego I. Gallardo ◽  
Mário de Castro ◽  
Héctor W. Gómez
Keyword(s):  
Estimation Method ◽  
Selection Criterion ◽  
Likelihood Method ◽  
Simulation Studies ◽  
Cure Rate ◽  
Nested Models ◽  
Proposed Model ◽  
The Em Algorithm ◽  
Competing Causes ◽  
The One

A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to covariates. Parameter estimation is based on the maximum likelihood method. Estimates are computed via the EM algorithm. In order to compare different models, a selection criterion for non-nested models is implemented. Results from simulation studies indicate that the estimation method and the model selection criterion have a good performance. A dataset on melanoma is analyzed using the proposed model as well as some models from the literature.

Optimization of a Novel CBCT Estimation Method using Prior Information

2010 ◽  
Vol 78 (3) ◽  
pp. S23
Author(s):  
L. Ren ◽  
J. Jin ◽  
B. Movsas ◽  
I.J. Chetty
Keyword(s):  
Prior Information ◽  
Estimation Method

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

scholarly journals Multivariate fractional phase–type distributions

2020 ◽  
Vol 23 (5) ◽  
pp. 1431-1451 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Martin Bladt ◽  
Mogens Bladt
Keyword(s):  
Tail Dependence ◽  
Jump Process ◽  
Multivariate Distributions ◽  
New Class ◽  
Natural Time ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Markovian Jump Process ◽  
Heavy Tailed

Abstract We extend the Kulkarni class of multivariate phase–type distributions in a natural time–fractional way to construct a new class of multivariate distributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals. The approach relies on assigning rewards to a non–Markovian jump process with ML sojourn times. This new class complements an earlier multivariate ML construction [2] and in contrast to the former also allows for tail dependence. We derive properties and characterizations of this class, and work out some special cases that lead to explicit density representations.

Estimation of the Shape Evolution and the Growth History of an Embedded Crack by Fatigue Loading

2011 ◽  
Author(s):  
Koji Gotoh ◽  
Keisuke Harada ◽  
Yosuke Anai
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Fatigue Cracks ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Fatigue Loading ◽  
Shape Evolution ◽  
Crack Growth Behaviour ◽  
Embedded Crack

Fatigue life estimation for planar cracks, e.g. part-through surface cracks or embedded cracks is very important because most of fatigue cracks found in welded built-up structures show planar crack morphologies. Fatigue crack growth behaviour of an embedded crack in welded joints is investigated in this study. The estimation procedure of crack shape evolution for an embedded crack is introduced and validation of the estimation procedure of fatigue crack growth based on the numerical simulation of fatigue crack growth with EDS concept for an embedded crack is performed. The validity of the proposed shape evolution estimation method and the fatigue crack growth simulation based on the fracture mechanics approach with EDS concept are confirmed.

Interlaced Attitude Estimation for Spacecraft Using Vector Observations

2021 ◽  
Vol 01 (03) ◽  
Author(s):  
Lubin Chang
Keyword(s):  
Prior Information ◽  
State Of The Art ◽  
Estimation Method ◽  
Attitude Estimation ◽  
The Body ◽  
Body Frame ◽  
Initial Value ◽  
Initial State ◽  
Initial Errors ◽  
Initial Attitude

This paper proposes an interlaced attitude estimation method for spacecraft using vector observations, which can simultaneously estimate the constant attitude at the very start and the attitude of the body frame relative to its initial state. The arbitrary initial attitude, described by constant attitude at the very start, is determined using quaternion estimator which requires no prior information. The multiplicative extended Kalman filter (EKF) is competent for estimating the attitude of the body frame relative to its initial state since the initial value of this attitude is exactly known. The simulation results show that the proposed algorithms could achieve better performance compared with the state-of-the-art algorithms even with extreme large initial errors. Meanwhile, the computational burden is also much less than that of the advanced nonlinear attitude estimators.

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