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Öğe A geometric process with Hjorth marginal: Estimation, discrimination, and reliability data modeling(Wiley, 2022) Demirci Bicer, Hayrinisa; Bicer, Cenker; Bakouch, Hassan Salah HassanThe geometric process is one of the important simple monotonic processes with a positive ratio parameter in the theory of stochastic processes. Simply, it can be thought of as a generalization of the renewal process (RP). In the current paper, we mainly study the geometric process with the Hjorth marginal distribution, with parameters theta and lambda, for being able to model the successive inter-arrival times with a trend. We first examine inference problem for the mentioned process from different perspectives and obtain the different estimators of its parameters by employing different estimation methods such as maximum likelihood, modified moments, modified maximum spacing, and modified least-squares. The efficiencies of these estimators are compared via a series of extensive simulation studies in the paper. Further, we give also a discrimination statistic for discriminating among geometric processes with the Hjorth distribution and its alternatives. This is quite important to select the optimal geometric process model for data. Finally, a modeling study by using the geometric process with the Hjorth distribution is provided in detail to display its effectiveness to model the reliability data sets.Öğe Block classical Gram-Schmidt-based block updating in low-rank matrix approximation(Scientific Technical Research Council Turkey-Tubitak, 2018) Erbay, Hasan; Varcin, Fatih; Horasan, Fahrettin; Bicer, CenkerLow-rank matrix approximations have recently gained broad popularity in scientific computing areas. They are used to extract correlations and remove noise from matrix-structured data with limited loss of information. Truncated singular value decomposition (SVD) is the main tool for computing low-rank approximation. However, in applications such as latent semantic indexing where document collections are dynamic over time, i.e. the term document matrix is subject to repeated updates, SVD becomes prohibitive due to the high computational expense. Alternative decompositions have been proposed for these applications such as low-rank ULV/URV decompositions and truncated ULV decomposition. Herein, we propose a BLAS-3 compatible block updating truncated ULV decomposition algorithm based on the block classical Gram-Schmidt process. The simulation results presented show that the block update algorithm is promising.Öğe Diagnosing breast cancer tumors using stacked ensemble model(Ios Press, 2022) Yurttakal, Ahmet Hasim; Erbay, Hasan; Ikizceli, Turkan; Karacavus, Seyhan; Bicer, CenkerBreast cancer is the most common cancer that progresses from cells in the breast tissue among women. Early-stage detection could reduce death rates significantly, and the detection-stage determines the treatment process. Mammography is utilized to discover breast cancer at an early stage prior to any physical sign. However, mammography might return false-negative, in which case, if it is suspected that lesions might have cancer of chance greater than two percent, a biopsy is recommended. About 30 percent of biopsies result in malignancy that means the rate of unnecessary biopsies is high. So to reduce unnecessary biopsies, recently, due to its excellent capability in soft tissue imaging, Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) has been utilized to detect breast cancer. Nowadays, DCE-MRI is a highly recommended method not only to identify breast cancer but also to monitor its development, and to interpret tumorous regions. However, in addition to being a time-consuming process, the accuracy depends on radiologists' experience. Radiomic data, on the other hand, are used in medical imaging and have the potential to extract disease characteristics that can not be seen by the naked eye. Radiomics are hard-coded features and provide crucial information about the disease where it is imaged. Conversely, deep learning methods like convolutional neural networks(CNNs) learn features automatically from the dataset. Especially in medical imaging, CNNs' performance is better than compared to hard-coded features-based methods. However, combining the power of these two types of features increases accuracy significantly, which is especially critical in medicine. Herein, a stacked ensemble of gradient boosting and deep learning models were developed to classify breast tumors using DCE-MRI images. The model makes use of radiomics acquired from pixel information in breast DCE-MRI images. Prior to train the model, radiomics had been applied to the factor analysis to refine the feature set and eliminate unuseful features. The performance metrics, as well as the comparisons to some well-known machine learning methods, state the ensemble model outperforms its counterparts. The ensembled model's accuracy is 94.87% and its AUC value is 0.9728. The recall and precision are 1.0 and 0.9130, respectively, whereas F1-score is 0.9545.Öğe Estimation procedures on Type-II censored data from a scaled Muth distribution(Yildiz Technical Univ, 2021) Bicer, Hayrinisa Demirci; Ozturker, Berkay; Bicer, CenkerIn the present paper, we consider the estimation problem for the scaled Muth distribution under Type-II censoring scheme. In order to estimate the model parameters alpha and beta, the maximum likelihood, the least-squares, and the maximum spacing estimators are derived. To show estimation efficiencies of the estimators obtained with this paper, we present an extensive Monte-Carlo simulation study in which the estimators are compared according to bias and mean squared error criteria. Furthermore, we evaluate the applicability of the scaled Muth distribution by taking into account both full and Type-II censored data situations by an analysis conducted on a real-life dataset.Öğe A new wrapped exponential distribution(Springer Heidelberg, 2018) Yilmaz, Abdullah; Bicer, CenkerWe introduce a new wrapped exponential distribution named transmuted wrapped exponential (TWE) distribution, for the modeling of circular datasets by using the Transmutation Rank-Map method. This method is employed for the first time for a wrapped distribution with this study. The introduced distribution is more flexible than traditional wrapped exponential distribution. The paper provides the explicit form of important distributional properties of the introduced distribution such as expectation, median, moments, characteristic function, quantile function, hazard rate function and stress-strength reliability. Renyi and Shannon entropies are also obtained. The statistical inference problem for the TWE distribution is investigated using maximum likelihood, least squares and weighted least squares and comparative numerical study results are presented. Furthermore, we present a real dataset analysis.Öğe Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor(Sciendo, 2016) Bicer, Cenker; Ozbek, Levent; Erbay, HasanIn this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non-linear discrete-time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter's stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable. The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.Öğe STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE GENERALIZED RAYLEIGH DISTRIBUTION(Univ Nis, 2020) Bicer, Cenker; Bicer, Hayrinisa D.; Kara, Mahmut; Yilmaz, AsumanIn the present paper, the statistical inference problem is considered for the geometric process (GP) by assuming the distribution of the first arrival time with generalized Rayleigh distribution with the parameters alpha and lambda. We have used the maximum likelihood method for obtaining the ratio parameter of the GP and distributional parameters of the generalized Rayleigh distribution. By a series of Monte-Carlo simulations evaluated through the different samples of sizes - small, moderate and large, we have also compared the estimation performances of the maximum likelihood estimators with the other estimators available in the literature such as modified moment, modified L-moment, and modified least squares. Furthermore, wehave presented two real-life datasets analyses to show the modeling behavior of GP with generalized Rayleigh distribution.Öğe Statistical Inference for Geometric Process with the Power Lindley Distribution(Mdpi, 2018) Bicer, CenkerThe geometric process (GP) is a simple and direct approach to modeling of the successive inter-arrival time data set with a monotonic trend. In addition, it is a quite important alternative to the non-homogeneous Poisson process. In the present paper, the parameter estimation problem for GP is considered, when the distribution of the first occurrence time is Power Lindley with parameters alpha and lambda. To overcome the parameter estimation problem for GP, the maximum likelihood, modified moments, modified L-moments and modified least-squares estimators are obtained for parameters a, alpha and lambda. The mean, bias and mean squared error (MSE) values associated with these estimators are evaluated for small, moderate and large sample sizes by using Monte Carlo simulations. Furthermore, two illustrative examples using real data sets are presented in the paper.Öğe Unit Maxwell-Boltzmann Distribution and Its Application to Concentrations Pollutant Data(Mdpi, 2024) Bicer, Cenker; Bakouch, Hassan S.; Bicer, Hayrinisa Demirci; Alomair, Gadir; Hussain, Tassaddaq; Almohisen, AmalIn the vast statistical literature, there are numerous probability distribution models that can model data from real-world phenomena. New probability models, nevertheless, are still required in order to represent data with various spread behaviors. It is a known fact that there is a great need for new models with limited support. In this study, a flexible probability model called the unit Maxwell-Boltzmann distribution, which can model data values in the unit interval, is derived by selecting the Maxwell-Boltzmann distribution as a base-line model. The important characteristics of the derived distribution in terms of statistics and mathematics are investigated in detail in this study. Furthermore, the inference problem for the mentioned distribution is addressed from the perspectives of maximum likelihood, method of moments, least squares, and maximum product space, and different estimators are obtained for the unknown parameter of the distribution. The derived distribution outperforms competitive models according to different fit tests and information criteria in the applications performed on four actual air pollutant concentration data sets, indicating that it is an effective model for modeling air pollutant concentration data.
