Browsing by Author "Aydogdu, Halil"

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Estimation of the Parameters of the Gamma Geometric Process
(Taylor & Francis Ltd, 2022) Kara, Mahmut; Guven, Gamze; Senoglu, Birdal; Aydogdu, Halil
There is no doubt that finding the estimators of model parameters accurately and efficiently is very important in many fields. In this study, we obtain the explicit estimators of the unknown model parameters in the gamma geometric process (GP) via the modified maximum likelihood (MML) methodology. These estimators are as efficient as maximum likelihood (ML) estimators. The marginal and joint asymptotic distributions of the MML estimators are also derived and efficiency comparisons between ML and MML estimators are made through an extensive Monte Carlo simulations. Moreover, a real data example is considered to illustrate the performances of the MML estimators together with their ML counterparts. According to simulation results, the performances of MML and ML estimators are close to each other even for small sample sizes.
Parameter Estimation in Α-Series Process With Lognormal Distribution
(Taylor & Francis inc, 2019) Kara, Mahmut; Altindag, Omer; Pekalp, Mustafa Hilmi; Aydogdu, Halil
The -series process (ASP) is widely used as a monotonic stochastic model in the reliability context. So the parameter estimation problem in an ASP is of importance. In this study parameter estimation problem for the ASP is considered when the distribution of the first occurrence time of an event is assumed to be lognormal. The parameters and of the ASP are estimated via maximum likelihood (ML) method. Asymptotic distributions and consistency properties of these estimators are derived. A test statistic is conducted to distinguish the ASP from renewal process (RP). Further, modified moment (MM) estimators are proposed for the parameters and and their consistency is proved. A nonparametric (NP) novel method is presented to test whether the ASP is a suitable model for data sets. Monte Carlo simulations are performed to compare the efficiencies of the ML and MM estimators. A real life data example is also studied to illustrate the usefulness of the ASP.
Statistical Inference for Geometric Process With the Rayleigh Distribution
(Ankara Univ, Fac Sci, 2019) Bicer, Cenker; Bicer, Hayrinisa Demirci; Kara, Mahmut; Aydogdu, Halil
The aim of this study is to investigate the solution of the statistical inference problem for the geometric process (GP) when the distribution of first occurrence time is assumed to be Rayleigh. Maximum likelihood (ML) estimators for the parameters of GP, where a and lambda are the ratio parameter of GP and scale parameter of Rayleigh distribution, respectively, are obtained. In addition, we derive some important asymptotic properties of these estimators such as normality and consistency. Then we run some simulation studies by different parameter values to compare the estimation performances of the obtained ML estimators with the non-parametric modified moment (MM) estimators. The results of the simulation studies show that the obtained estimators are more efficient than the MM estimators.
Statistical Inference for Α-Series Process With Gamma Distribution
(Taylor & Francis inc, 2017) Kara, Mahmut; Aydogdu, Halil; Senoglu, Birdal
The explicit estimators of the parameters alpha, mu and sigma(2) are obtained by using the methodology known as modifiedmaximum likelihood (MML) when the distribution of the first occurrence time of an event is assumed to be Weibull in series process. The efficiencies of the MML estimators are compared with the corresponding nonparametric (NP) estimators and it is shown that the proposed estimators have higher efficiencies than the NP estimators. In this study, we extend these results to the case, where the distribution of the first occurrence time is Gamma. It is anotherwidely used andwell-known distribution in reliability analysis. A real data set taken fromthe literature is analyzed at the end of the study for better understanding the methodology presented in this paper.
Statistical Inference for Α-Series Process With the Inverse Gaussian Distribution
(Taylor & Francis inc, 2017) Kara, Mahmut; Turksen, Ozlem; Aydogdu, Halil
Statistical inferences for the geometric process (GP) are derived when the distribution of the first occurrence time is assumed to be inverse Gaussian (IG). An alpha-series process, as a possible alternative to the GP, is introduced since the GP is sometimes inappropriate to apply some reliability and scheduling problems. In this study, statistical inference problem for the alpha-series process is considered where the distribution of first occurrence time is IG. The estimators of the parameters alpha, mu, and sigma(2) are obtained by using the maximum likelihood (ML) method. Asymptotic distributions and consistency properties of the ML estimators are derived. In order to compare the efficiencies of the ML estimators with the widely used nonparametric modified moment (MM) estimators, Monte Carlo simulations are performed. The results showed that the ML estimators are more efficient than the MM estimators. Moreover, two real life datasets are given for application purposes.
A Study on Comparisons of Bayesian and Classical Parameter Estimation Methods for the Two-Parameter Weibull Distribution
(Ankara Univ, Fac Sci, 2020) Yilmaz, Asuman; Kara, Mahmut; Aydogdu, Halil
The main objective of this paper is to determine the best estimators of the shape and scale parameters of the two parameter Weibull distribution. Therefore, both classical and Bayesian approximation methods are considered. For parameter estimation of classical approximation methods maximum likelihood estimators (MLEs), modified maximum likelihood estimators-I (MMLEs-I), modified maximum likelihood estimators-II (MMLEs-II), least square estimators (LSEs), weighted least square estimators (WLSEs), percentile estimators (PEs), moment estimators (MEs), L-moment estimators (LMEs) and TL-moment estimators (TLMEs) are used. Since the Bayesian estimators don't have the explicit form. There are Bayes estimators are obtained by using Lindley's and Tierney Kadane's approximation methods in this study. In Bayesian approximation, the choice of loss function and prior distribution is very important. Hence, Bayes estimators are given based on both the non-informative and informative prior distribution. Moreover, these estimators have been calculated under different symmetric and asymmetric loss functions. The performance of classical and Bayesian estimators are compared with respect to their biases and MSEs through a simulation study. Finally, a real data set taken from Turkish State Meteorological Service is analysed for better understanding of methods presented in this paper.