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    A COMPARISON OF THE STATISTICAL DISTRIBUTIONS OF AIR POLLUTION CONCENTRATIONS IN SINOP, TURKEY
    (Technical Univ Wroclaw, 2024) Aydin, Demet
    The increasing population and industrialization are the reasons for environmental and air pollution around the world. Air pollution is a major threat, especially to human health, both biological and economic. Therefore, determining the properties of air pollutants is very important for researchers and practitioners working in this field. In this study, the statistical distributions of some air pollutants are determined using the Gumbel, Weibull, generalized Pareto, log-normal, gamma, Rayleigh, and inverse Weibull distributions. The data was obtained from stations Boyabat and Merkez stations in Sinop province in 2017. The Kolmogorov-Smirnov test was used to determine the underlying distributions of the air pollution data. Then we use the root mean square error and coefficient of determination criteria to determine which distribution better fits the air pollution data. Finally, numerical results have shown that the generalized Pareto distribution demonstrates the best overall modeling performance, followed by log-normal and inverse Weibull distributions.
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    Alternative robust estimation methods for parameters of Gumbel distribution: an application to wind speed data with outliers
    (Techno-Press, 2018) Aydin, Demet
    An accurate determination of wind speed distribution is the basis for an evaluation of the wind energy potential required to design a wind turbine, so it is important to estimate unknown parameters of wind speed distribution. In this paper, Gumbel distribution is used in modelling wind speed data, and alternative robust estimation methods to estimate its parameters are considered. The methodologies used to obtain the estimators of the parameters are least absolute deviation, weighted least absolute deviation, median/MAD and least median of squares. The performances of the estimators are compared with traditional estimation methods (i.e., maximum likelihood and least squares) according to bias, mean square deviation and total mean square deviation criteria using a Monte-Carlo simulation study for the data with and without outliers. The simulation results show that least median of squares and median/MAD estimators are more efficient than others for data with outliers in many cases. However, median/MAD estimator is not consistent for location parameter of Gumbel distribution in all cases. In real data application, it is firstly demonstrated that Gumbel distribution fits the daily mean wind speed data well and is also better one to model the data than Weibull distribution with respect to the root mean square error and coefficient of determination criteria. Next, the wind data modified by outliers is analysed to show the performance of the proposed estimators by using numerical and graphical methods.
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    ESTIMATING THE MISSING VALUE IN ONE-WAY ANOVA UNDER LONG-TAILED SYMMETRIC ERROR DISTRIBUTIONS
    (Yildiz Technical Univ, 2018) Aydin, Demet; Senoglu, Birdal
    In practice, missing values are widely seen and create serious problems in almost all statistical analysis. In this study, to deal with missing values, we propose estimators for missing value in one-way analysis of variance (ANOVA) when the distribution of error terms is long-tailed symmetric (LTS). We use methodologies known as maximum likelihood (ML), modified maximum likelihood (MML) and least squares (LS) in estimating missing value. Expectation and maximization (EM) algorithm is used for computing ML estimate of missing value. We compare the efficiencies of LS, ML and MML estimators of missing value via Monte Carlo simulation study. Simulation results show that ML estimator of missing value is the most efficient among the others. The usefulness of the proposed estimators is illustrated by peak discharge data example taken from civil engineering.
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    Monte Carlo Comparison of the Parameter Estimation Methods for the Two-Parameter Gumbel Distribution
    (Wayne State Univ Press, 2015) Aydin, Demet; Senoglu, Birdal
    The performances of the seven different parameter estimation methods for the Gumbel distribution are compared with numerical simulations. Estimation methods used in this study are the method of moments (ME), the method of maximum likelihood (ML), the method of modified maximum likelihood (MML), the method of least squares (LS), the method of weighted least squares (WLS), the method of percentile (PE) and the method of probability weighted moments (PWM). Performance of the estimators is compared with respect to their biases, MSE and deficiency (Def) values via Monte-Carlo simulation. A Monte Carlo Simulation study showed that the method of PWM was the best performance the other methods of bias criterion and the method of ML outperforms the other methods in terms of Def criterion. A real life example taken from the hydrology literature is given at the end of the paper.
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    Performance evaluation of estimators in the presence of outliers or omitted predictors: a study on the Poisson-Exponential regression model
    (Taylor & Francis Inc, 2023) Altinisik, Yasin; Aydin, Demet
    The Poisson regression model is vulnerable for overdispersion in the data when estimating model parameters and their standard errors. Overdispersion may occur due to outliers in the data and/or removal of important predictors from the model. This paper employs a regression model that can be used to better cope with outliers and omitted predictor bias in count data compared to the Poisson regression model, namely the Poisson exponential (PE) model which is a reparameterization of the geometric regression model. Along with investigating the distributional properties of the PE distribution, the usual maximum likelihood (ML-I), maximum likelihood with Expectation-maximization algorithm (ML-II), least-square (LS), weighted least-square (WLS), least-absolute deviation (LAD), weighted least-absolute deviation (WLAD), and Cramer-von mises (CVM) estimation methods are utilized in the context of the PE regression model. The performance of these estimation methods with the PE regression model are inspected through two comprehensive simulation studies. The first is conducted on data sets with and without outliers. The second investigates the performance of the estimation methods for the PE regression model with and without omitted predictors. Two real-life applications illustrate the applicability of the PE regression model with the estimation methods for these two situations.
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    Robust estimation of the location and the scale parameters of shifted Gompertz distribution
    (Univ Studi Salento, 2018) Aydin, Demet; Akgul, Fatma Gul; Senoglu, Birdal
    In this study, we consider the estimation of the location parameter mu and the scale parameter sigma of the shifted Gompertz distribution. We obtain the closed form estimators of these parameters by using the modified maximum likelihood methodology. We also compare the efficiencies of these estimators with the well-known and widely used least squares and maximum likelihood estimators via Monte-Carlo simulation study in terms of bias, mean square error and deficiency criteria. In addition, we evaluate the performances of the proposed estimators when the data set contains outliers or is contaminated. In other words, the robustness properties of the estimators are investigated. A real data set is analyzed to demonstrate the implementation of the estimation methods at the end of the study.
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    THE NEW WEIGHTED INVERSE RAYLEIGH DISTRIBUTION AND ITS APPLICATION
    (Univ Nis, 2019) Aydin, Demet
    In this study, a new weighted version of the inverse Rayleigh distribution based on two different weight functions is introduced. Some statistical and reliability properties of the introduced distribution including the moments, moment generating function, entropy measures (i.e., Shannon and Renyi) and survival and hazard rate functions are derived. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms. So, a numerical method has been required to compute maximum likelihood estimates. Finally, the daily mean wind speed data set has been analysed to show the usability of the new weighted inverse Rayleigh distribution.
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    WEIGHTED VARIABLE EXPONENT LEBESGUE SPACES ON A PROBABILITY SPACE
    (Editura Bibliotheca-Bibliotheca Publ House, 2023) Aydin, Ismail; Aydin, Demet
    In this paper, we introduce the weighted variable exponent Lebesgue spaces defined on a probability space and give some information about the martingale theory of these spaces. We first prove several basic inequalities for expectation operators and obtain several norm convergence conditions for martingales in weighted variable exponent Lebesgue spaces. We discuss the H & ouml;lder inequality and embedding properties in these spaces. Finally, under some conditions we investigate Doob's maximal function.