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    Öğe
    STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE GENERALIZED RAYLEIGH DISTRIBUTION
    (Univ Nis, 2020) Bicer, Cenker; Bicer, Hayrinisa D.; Kara, Mahmut; Yilmaz, Asuman
    In 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.
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    Öğe
    STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE RAYLEIGH DISTRIBUTION
    (2019) Biçer, Cenker; Biçer, Hayrinisa Demirci; Kara, Mahmut; Aydoğdu, 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 Örst occurrence time is assumed to be Rayleigh. Maximum likelihood (ML) estimators for the parameters of GP, where a and ? 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 di§erent parameter values to compare the estimation performances of the obtained ML estimators with the non-parametric modiÖed moment (MM) estimators. The results of the simulation studies show that the obtained estimators are more e¢ cient than the MM estimators.