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- MakaleYalnız künye2026Scopus SJRQ2A Bernstein polynomial estimation of the moment generating function
Susam, Selim Orhun
We study Bernstein polynomial smoothing for nonparametric estimation of the moment generating function (MGF) of a distribution supported on (Formula presented.). We prove strong consistency of the Bernstein-smoothed MGF estimator and show that, when the smoothing degree m grows sufficiently fast, it shares the same (Formula presented.) asymptotic normal distribution as the empirical MGF estimator, with variance (Formula presented.). A second-order bias–variance expansion reveals that Bernstein smoothing yields a bias of order (Formula presented.) and a variance-reduction term of order (Formula presented.). This leads to the optimal smoothing rate (Formula presented.) for pointwise mean squared error (MSE) minimization. Simulation results confirm that the Bernstein estimator is especially effective in challenging boundary-dominated settings, notably for U-shaped beta models and for larger positive t values. Overall, Bernstein polynomial smoothing provides a simple, theoretically justified, and practically effective tool for nonparametric MGF estimation on compact supports.
- MakaleYalnız künye2026Scopus SJRQ2A bias-corrected partial bernstein copula approach for nonparametric regression
Susam, Selim Orhun
Multivariate Bernstein polynomials yield smooth, boundary–bias–free estimators for copulas and their derivatives. The classical partial Bernstein copula derivative of Janssen et al. (2016) suffers from an uncorrected first–order bias that can dominate the mean squared error (MSE) in moderate samples. We introduce a simple double–difference correction that removes the entire leading bias term while increasing the variance by a small fixed multiplicative factor only. When this bias–reduced partial derivative is plugged into the copula based regression integral, the resulting estimator achieves substantially smaller bias and uniformly lower MSE than the classical version. Analytic bias–variance expansions are provided, and a comprehensive Monte Carlo study shows up to 50% reductions in MSE across a range of Bernstein copula degrees. A real data application to the mcycle dataset further demonstrates the practical advantages of the method, with the smoothing parameters selected by least squares cross validation (LSCV).
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İncele - MakaleYalnız künye2026Scopus SJRQ3A multi-parametric unit distribution via Bernstein polynomials
Susam, Selim Orhun
This study develops the method of constructing a multi-parametric distribution on the unit interval using Bernstein polynomials and investigates its key statistical properties. The performance of the proposed distribution’s parameter estimators was evaluated by Monte Carlo simulation under both maximum-likelihood (MLE) and minimum-distance frameworks, with the MLE approach generally yielding lower estimation error. A real data example illustrates the advantages of the construction method. The results reveal that the Bernstein distribution provides superior goodness-of-fit to the dataset compared with competing models.
- MakaleAçık Erişim2026Scopus SJRQ2Risk Assessment via Hazard Scenario in Cereal Production Under Rising CO
Susam, Selim Orhun; Peker, Ayse Esra; Hudaverdi, Burcu
Global food security has been seriously threatened by air pollution and climate change. The impact of CO on crop output is complicated because of its interactions with temperature, nutrient availability, and other pollutants, even though it is necessary for photosynthesis. This study develops a copula-based hazard modeling framework to assess how increasing CO concentrations affect cereal production risk across multiple crops. By integrating hazard scenario analysis with localized dependence measures, we estimate both failure probabilities and dynamic associations between CO emissions and cereal yields. A novel localized version of Kendall’s implemented via a Bernstein copula approximation, enables flexible modeling of heterogeneous and nonlinear dependence structures. As the relationship between CO emissions and crop-specific yields changes in both density and direction, it may indicate asymmetries or nonlinearities that are missed by measures of global dependence. Empirical results reveal distinct crop-specific responses. While CO levels enhance yields for rice, millet, and sugar beet, they reduce or destabilize production for rye and lentil, indicating asymmetric sensitivities. Failure probabilities increase with the time horizon, reflecting the accumulation of climate-related production risk. The findings emphasize the significance of integrating probabilistic hazard modeling into climate-resilient agricultural planning and food security policies, as crop-specific risk exposure has increased in recent time periods.
AtıfWoS1OpenAlex1İncele - MakaleYalnız künye2025Scopus SJRQ2Copula-based conditional reliability with application to rocket motor data
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.
AtıfScopus4WoS5OpenAlex5İncele - MakaleYalnız künye2025Scopus SJRQ4Spearman dependence function-based goodness-of-fit test for the gene's relation
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.
AtıfScopus2WoS2OpenAlex2İncele - MakaleYalnız künye2025Scopus SJRQ2A flexible parameter estimation method for the Farlie-Gumbel-Morgenstern copula: a simulation study
Susam, Selim Orhun
This research presents a minimum distance method based on the Bernstein empirical copula process for estimating the dependence parameter of the Farlie-Gumbel-Morgenstein copula. Also, this study examines its performance through a comprehensive Monte Carlo simulation study. The findings in this paper demonstrate that selecting the optimal degree of the Bernstein empirical copula has a significant impact on the performance of the new estimation method. The proposed estimator achieves optimal performance in terms of mean squared error (MSE) for the parameter range (Formula presented.) in small sample sizes, while outside this range, its performance varies depending on the degree of the Bernstein empirical copula. Finally, we apply the new method to real data for illustrative purposes.
AtıfScopus3WoS4OpenAlex3İncele - MakaleYalnız künye2024Scopus SJRQ2Stress–strength reliability for electricity systems based on the Bernstein copula approximation
Susam, Selim Orhun; Hudaverdi, Burcu
Electricity is a critical resource for modern society, and its availability is essential for various aspects of daily life, from powering homes to supporting industrial processes and infrastructure. Ensuring a reliable supply of electricity is vital for economic stability and the well-being of a population. As the world moves toward more sustainable and renewable energy sources, understanding the reliability of these sources compared to traditional fossil fuels is crucial. In this study, we develop a methodology that enables the measurement of stress–strength reliability when electricity consumption is considered as the strength variable, positioned between electricity generation from renewable energy sources and fossil fuels as stress variables. We achieve this using the copula-based reliability with Bernstein copula approximation. The methodology is applied to the U.S. monthly electricity data. The result shows that the current rates of electricity output from fossil fuels and renewables will not be sufficient to meet the demand for electricity.
AtıfScopus2WoS3OpenAlex3İncele - MakaleYalnız künye2024Scopus SJRQ3On the Construction of a Semiparametric Family of Bivariate Copulas Using the Opposite Diagonal Section of Copulas
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.
AtıfScopus1WoS1OpenAlex1İncele - MakaleYalnız künye2024Scopus SJRQ4A Note on a New Bivariate Copula Defined with a Piecewise Generator Function
Chesneau, Christophe; Susam, Selim Orhun
Copulas are essential probability tools for characterizing the joint distribution of random variables. In this article, we contribute to the topic by studying special bivariate copulas. They have the property of being defined with piecewise components and are designed for the analysis of data that have dependence structures with distinct substructures in square zones. The theoretical properties of the copulas are studied, with emphasis on their mathematical validity and some dependence measures. In particular, it is shown that the Kendall tau coefficient has a simple expression that is governed by several parameters, demonstrating the flexibility of the approach. In addition, a real data example is provided to demonstrate the applicability of the copulas. Fair comparisons with other standard copulas motivate their use in other practical scenarios.
- MakaleYalnız künye2023Scopus SJRQ2A weighted independence test based on smooth estimation of Kendall distribution
Susam, Selim Orhun; Hudaverdi, Burcu
In this study, we introduce a nonparametric test of independence which is based on a weighted Cramér-von Mises distance of the Bernstein estimate of the Kendall distribution function. We examine the power and the size of the new weighted test and, we compare it with the non-weighted nonparametric tests of independence through a Monte Carlo simulation study. The simulation results indicate that both of the choices of the weights and the polynomial degree has a significant effect on the test power. Finally, the procedure is applied to a dataset on chemical elements in water samples for the purpose of illustration.
AtıfScopus1WoS1OpenAlex1İncele - MakaleYalnız künye2023Scopus SJRQ3On the weighted tests of independence based on Bernstein empirical copula
Hudaverdi, Burcu; Susam, Selim Orhun
In this article, we propose a flexible weighted test of independence based on Cramér-von Mises statistic of the Bernstein empirical copula process. We investigate the asymptotic properties of the new weighted test. A Monte Carlo study is conducted to measure the power performance of the new test under various dependence structures and also to compare the performance with some other alternative tests. The effects of the weights and the selection of optimal Bernstein polynomial degree are significantly influencing the power of the test according to the particular type of dependence. Finally, the procedure is also applied to a dataset on diabetes for illustrative purpose.
AtıfScopus8WoS8OpenAlex7İncele - MakaleYalnız künye2023Scopus SJRQ3A goodness-of fit improvement based on τ-preserving transformation for semiparametric family of copulas
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.
AtıfScopus3WoS3OpenAlex2İncele - MakaleYalnız künye2023Scopus SJRQ2On the copula-based reliability of stress-strength model under bivariate stress
Hudaverdi, Burcu; Susam, Selim Orhun
In this paper, we consider the stress-strength reliability (Formula presented.) where the strength Y of a component lies between the dependent stress variables (Formula presented.) and (Formula presented.). We propose a copula-based approach for stress-strength reliability having bivariate stress. We obtain R for Farlie-Gumbel-Morgenstern copula with Burr III marginals. Also, we propose a Bernstein copula approximation for evaluating R under the stress-strength setup. We present empirical and maximum likelihood-based estimation procedures and compare their performances by Monte Carlo simulation. We apply the proposed approach to chemical and overt diabetes data for illustration purpose.
AtıfScopus12WoS12OpenAlex11İncele - MakaleYalnız künye2022On the Archimedean copula constructed from the Bezier polynomial type diagonal section
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.
- MakaleAçık Erişim2022TAIL DEPENDENCE ESTIMATION BASED ON SMOOTH ESTIMATION OF DIAGONAL SECTION
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.
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İncele - MakaleAçık Erişim2022Scopus SJRQ3A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial
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.
AtıfScopus16WoS15OpenAlex15İncele - MakaleYalnız künye2022Scopus SJRQ3Plug-in Estimation of Dependence Characteristics of Archimedean Copula via Bézier Curve
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.
AtıfScopus1WoS1İncele - MakaleAçık Erişim2020Scopus SJRQ4Parameter estimation of some archimedean copulas based on minimum cramer-von-mises distance
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.
AtıfScopus13WoS9OpenAlex10İncele - MakaleAçık Erişim2020Scopus SJRQ3A new family of archimedean copula via trigonometric generator function
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.
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