Hudaverdi, Burcu; Susam, Selim Orhun; Chesneau, Christophe

In this paper, we construct conditional reliability in the context of stress-strength models, taking into account the relationship between applied stress and strength. The Bernstein copula approximation is used to calculate the conditional reliability values. Real data from a rocket motor experiment are considered to evaluate the conditional reliability strength of a motor case and the required stress endurance for the motor.

AtıfScopus4·WoS5·OpenAlex5

İncele

Susam, Selim Orhun; Hudaverdi, Burcu

A gene network represents the relationship between different groups of genes with various functions, aiming to depict how genes collaborate and influence each other’s activities within a biological system. This relationship can be effectively explained using copulas. Therefore, it is crucial to determine which copula best fits the gene data and provide the most accurate explanation of the relationships between gene groups. In this study, our objective is to introduce a Spearman dependence function-based goodness-of-fit test using Bernstein polynomial approximation. We apply this test to identify a copula model that can effectively explain the relationships between gene groups. A Monte Carlo simulation study is conducted to assess the performance of the proposed test. Next, we analyse histone gene groups using data from yeast cell regulation, as provided by Eisen et al. (1998). Specifically, we investigate the dependence model structures of gene interactions for eight histone genes.

AtıfScopus2·WoS2·OpenAlex2

İncele

Susam, Selim Orhun; Chesneau, Christophe

In this article, a new semiparametric family of bivariate copulas is proposed and studied. The copulas of this family innovate in their construction; they are based on an original univariate generating function involving the opposite diagonal section of intermediary copulas. Several of their crucial properties are examined. In the practical part, we use them to estimate the reliability parameter in a stress-strength-dependent setting, including an estimation approach based on the Bernstein copula. Finally, their applicability and good performance are confirmed using a data set related to the logarithmic concentrations of two chemical elements in water samples.

AtıfScopus1·WoS1·OpenAlex1

İncele

Susam, Selim Orhun; Hudaverdi, Burcu

In this paper, we study on improving the goodness-of fit for the data by using τ-preserving transform for the semiparametric family of bivariate copulas. We estimate the generator function (Formula presented.) using the Bézier polynomial function and define τ- preserving transformation on the generator function under positive quadrant dependence assumption. We investigate the performance of our methodology on real data example contained life expectancy study. The findings indicate that the model fitting is improved by using τ- preserving transformation.

AtıfScopus3·WoS3·OpenAlex2

İncele

Susam, Selim Orhun

In this study, we construct a convex Bezier type diagonal section which uniquely characterizes the Archimedean copula. The proposed diagonal section is flexible according to its polynomial degree; hence, we can add the additional parameters to the diagonal section by increasing the polynomial degree. We also present a graphical tool based on the diagonal section in order to visualize the different types of Archimdean copulas in the copula test space. As an illustration, the real data examples are given.

İncele

Susam, Selim Orhun

This paper is mainly developed around the diagonal section which is strongly related to tail dependence coefficients as defined in Nelsen [19]. Hence, we propose a flexible method for estimating tail dependence coefficients based on the new smooth estimation of the diagonal section based on the Bernstein polynomial approximation. To assess the performance of the new estimators we conduct the Monte-Carlo simulation study. As a result of the simulation study, both estimators perform satisfactory performance. Also, the estimation methods are illustrated by real data examples.

AtıfWoS1·OpenAlex1

İncele

Susam, Selim Orhun

In this paper, we are proposing a flexible method for constructing a bivariate generalized Farlie-Gumbel-Morgenstern (G-FGM) copula family. The method is mainly developed around the function ϕ(t) (t ∈ [0, 1]), where ϕ is the generator of the G-FGM copula. The proposed construction method has useful advantages. The first of which is the direct relationship between the ϕ function and Kendall’s tau. The second advantage is the possibility of constructing a multi-parameter G-FGM copula which allows us to better harmonize empirical instruction with the model. The construction method is illustrated by three real data examples.

AtıfScopus16·WoS15·OpenAlex15

İncele

Susam, Selim Orhun; Erdoğan, Mahmut Sami

• This article introduces measurement of the dependence between variables with a dependence structure defined by Archimedean copulas. The estimation of the dependence measure, such as Kendall’s tau as well as the lower and upper tail dependence, is investigated by using estimation of the Kendall distribution function based on the Bézier curve. A Monte Carlo study is performed to measure the performance of the new estimation method. The simulation results showed that the proposed methods has good results in terms of estimation performance. The new estimators are also used to estimate the dependence coefficients for three sets of real data.

AtıfScopus1·WoS1

İncele

Susam, Selim Orhun

The purpose of this paper is to introduce a new estimation method for estimating the Archimedean copula dependence parameter in the non-parametric setting. The estimation of the dependence parameter has been selected as the value that minimizes the Cramer-von-Mises distance which measures the distance between Empirical Bernstein Kendall distribution function and true Kendall distribution function. AMonte Carlo study is performedto measure the performance of thenewestimator and compared to conventional estimation methods. In terms of estimation performance, simulation results show that the proposed Minumum Cramer-von-Mises estimation method has a good performance for low dependence and a small sample size when compared with the other estimation methods. The new minimum distance estimation of the dependence parameter is applied to model the dependence of two real data sets.

AtıfScopus13·WoS9·OpenAlex10

İncele

Susam, Selim Orhun

In this paper, new type of Archimedean copula based on cotangent generator function, and dependence characteristics are investigated. Also, the estimation procedure of the dependence parameter is given. A Monte Carlo study is performed to measure the performance of estimators. To demonstrate the goodness of fit performance of the new family, a real data analysis is performed.

AtıfScopus13·WoS10·OpenAlex11·TR Dizin1

İncele