On Parameter Estimation with the Method of Moments

Öz

The method of moments uses to estimate the parameters of a statistical model. This method aims to find the values of the parameters which are solutions of equations given by relationship between the sample moments and the population moments. The Method of Moments, which is the first estimation method known in the literature, was first introduced by Pearson. This method is constantly used because of its applicability, simplicity and understanding. In this study, the estimators of the unknown parameters of the Binomial, Poisson, Continuous Uniform, and Gamma distributions are obtained by the Moments Method and the actual values and the estimation values are compared by simulating random data for the given distributions.

Anahtar Kelimeler

• Parameter Estimation
• Method of Moments
• Binomial Distribution
• Poisson Distribution
• Gamma Distribution

Momentler Metodu ile Parametre Tahmini Üzerine

Öz

Momentler Metodu, bir istatistiksel modelin parametrelerini tahmin etmek için kullanılır. Bu yöntem örnek momentleri ile anakütle momentleri arasındaki ilişki ile verilen denklemlerin çözümü ile parametrelerin değerlerini bulmayı amaçlar. Literatürde bilinen ilk tahmin yöntemi olan Momentler Metodu ilk olarak Pearson tarafından ortaya atılmıştır. Uygulanabilirliği, basit ve anlaşılır olmasından dolayı sürekli başvurulan bir yöntemdir. Bu çalışmada, Binom, Poisson, Sürekli Düzgün ve Gamma dağılımlarının bilinmeyen parametrelerinin tahmincileri Momentler Metodu ile elde edilmiş ve verilen dağılımlar için tesadüfi veriler simüle edilerek gerçek değerleri ile tahmin değerleri karşılaştırılmıştır.

Anahtar Kelimeler

• Parametre Tahmini
• Momentler Metodu
• Binom Dağılımı
• Poisson Dağılımı
• Gamma Dağılımı

Kaynakça

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