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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 Properties and Inference for a New Class of Generalized Rayleigh Distributions with an Application(Sciendo, 2019) Bicer, Hayrinisa DemirciIn the present paper, we introduce a new form of generalized Rayleigh distribution called the Alpha Power generalized Rayleigh (APGR) distribution by following the idea of extension of the distribution families with the Alpha Power transformation. The introduced distribution has the more general form than both the Rayleigh and generalized Rayleigh distributions and provides a better fit than the Rayleigh and generalized Rayleigh distributions for more various forms of the data sets. In the paper, we also obtain explicit forms of some important statistical characteristics of the APGR distribution such as hazard function, survival function, mode, moments, characteristic function, Shannon and Renyi entropies, stress-strength probability, Lorenz and Bonferroni curves and order statistics. The statistical inference problem for the APGR distribution is investigated by using the maximum likelihood and least-square methods. The estimation performances of the obtained estimators are compared based on the bias and mean square error criteria by a conducted Monte-Carlo simulation on small, moderate and large sample sizes. Finally, a real data analysis is given to show how the proposed model works in practice.Öğe Properties and inference for a new class of XGamma distributions with an application(Springer Heidelberg, 2019) Bicer, Hayrinisa DemirciThe current paper introduces a new flexible probability distribution model called transmuted XGamma distribution which pullulates from the XGamma distribution and possesses the characteristics of XGamma distribution in special cases. In the paper, we obtain the explicit expressions for some important statistical properties of the introduced distribution such as hazard rate and survival functions, mean residual life, moment-generating function, moments, skewness, kurtosis, distribution of its order statistics, Lorenz and Bonferroni curves. Besides obtaining the various effective estimators for the parameters of the distribution, estimation performances of these estimators are comparatively examined with a series of Monte Carlo simulations. Furthermore, to demonstrate the modeling ability of the proposed distribution on real-world phenomena, an illustrative example is performed by using an actual data set in connection with the field of the lifetime.Öğe Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution(Mdpi, 2019) Bicer, Hayrinisa DemirciIn the modeling of successive arrival times with a monotone trend, the alpha-series process provides quite successful results. Both selecting the distribution of the first arrival time and making an optimal statistical inference play a crucial role in the modeling performance of the alpha-series process. In this study, when the distribution of the first arrival time is the generalized Rayleigh, the problem of statistical inference for the alpha, beta, and gamma parameters of the alpha-series process is considered. Further, in order to obtain optimal modeling performance from the mentioned alpha-series process, various estimators for the model parameters are obtained by employing different estimation methodologies such as maximum likelihood, modified maximum spacing, modified least-squares, modified moments, and modified L-moments. By a series of Monte Carlo simulations, the estimation efficiencies of the obtained estimators are evaluated through the different sample sizes. Finally, two real datasets are analyzed to illustrate the importance of modeling with the alpha-series process.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.
