Multiple failure modes and strength degradation are usually inherent in the gear transmission system, which brings new challenges for conducting fatigue reliability analysis design. This paper proposes a novel dynamic method dependence based on combination of Copula function Gamma process. Firstly, simulation model system is established to obtain stress-time history. The process then used descr...

There is an infinite number of parameters in the definition of multivariate maxima of moving maxima (M4) processes, which poses challenges in statistical applications where workable models are preferred. This paper establishes sufficient conditions under which an M4 process with infinite number of parameters may be approximated by an M4 process with finite number of parameters. In statistical i...

Entropy is a measure of uncertainty and has been commonly used for various applications, including probability inferences in hydrology. Copula has been widely used for constructing joint distributions to model the dependence structure of multivariate hydrological random variables. Integration of entropy and copula theories provides new insights in hydrologic modeling and analysis, for which the...

Vine copula models have proven themselves as a very flexible class of multivariate copula models with regard to symmetry and tail dependence for pairs of variables. The full specification of a vine model requires the choice of vine tree structure, copula families for each pair copula term and their corresponding parameters. In this survey we discuss the different approaches, both frequentist as...

Accurately and adequately modelling and analyzing relationships in real random phenomena involving several variables are prominent areas in statistical data analysis. Applications of such models are crucial and lead to severe economic and financial implications in human society. Since the beginning of developments in Statistical methodology as the formal scientific discipline, correlation based...

With the aim of portfolio optimization and management, this article utilizes the Clayton-copula along with copula theory measures. Portfolio-Optimization is one of the activities in investment funds. Thus, it is essential to select an appropriate optimization method. In modern financial analyses, there is growing evidence indicating the distribution of proceeds of financial properties is not cu...

In information theory, mutual information (MI) is a difference concept with entropy.[1] In this paper, we prove with copula [2] that they are essentially same – mutual information is also a kind of entropy, called copula entropy. Based on this insightful result, We propose a simple method for estimating mutual information. Copula is a theory on dependence and measurement of association.[2] Skla...

We consider the problem of accurately measuring the credit risk of a portfolio consisting of loans, bonds and other financial assets. One particular performance measure of interest is the probability of large portfolio losses over a fixed time horizon. We revisit the so-called t-copula that generalizes the popular normal copula to allow for extremal dependence among defaults. By utilizing the a...

In this paper, a lexical functional grammar for an automatic classification of Urdu copula verb hO (be/become) is presented according to linguistic theories. A test suite of sentences containing almost all different conjugation forms of copula verb is extracted from a raw corpus. It is tried to keep only the cases of copular construction because the copula verb hO is very much dynamic in nature...

This paper presents algorithms for generating random variables for exponential/Rayleigh/ Weibull, Nakagami-m and Rician copulas with any desired copula parameter(s), using the direct conditional cumulative distribution function method and the complex Gaussian distribution method. Moreover, a novel method for optimal copula selection is also proposed, based on the criterion that for a given seri...