STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE GENERALIZED RAYLEIGH DISTRIBUTION

Cenker Biçer, Hayrinisa D. Biçer, Mahmut Kara, Asuman Yılmaz

DOI Number
https://doi.org/10.22190/FUMI2004107B
First page
1107
Last page
1125

Abstract


In the present paper, statistical inference problem is considered for the geometric process (GP) by assuming the distribution of the first arrival time is generalized Rayleigh with the parameters $\alpha$ and $\lambda$. We use 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 also compare 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, we present two real-life dataset analyzes to show the modeling behavior of GP with generalized Rayleigh distribution.

Keywords

Monotone processes; non-parametric estimation; parametric estimation; stochastic process; data with trend.

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DOI: https://doi.org/10.22190/FUMI2004107B

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