Using simulation to study the sampling distribution of some well known statistics

مقدم أطروحة جامعية

Rammahah, Huda Ibrahim

مشرف أطروحة جامعية

Dabeet, Ilyas

أعضاء اللجنة

Abu Libdih, Uthman
Araj, Simun

الجامعة

جامعة بيرزيت

الكلية

كلية العلوم

القسم الأكاديمي

دائرة الرياضيات

دولة الجامعة

فلسطين (الضفة الغربية)

الدرجة العلمية

ماجستير

تاريخ الدرجة العلمية

2004

الملخص الإنجليزي

The focus of this study is to use the probabilistic and the bootstrap simulation methods to investigate graphically, computationally and analytically the three main characteristics: location, spread and the shape of the sampling distribution of the three well known sample statistics : the sample mean, the sample median, and the 36 sample variance by varying the sample size and distribution of the underlying population.

The simulated results of this study can be summarized as follows : a) The sampling distribution of the sample mean, the sample median and the sample variance can be approximated by a normal distribution, with a very small bias, provided the sample size is large.

However, for small sample size, the normality of the sampling distribution of these statistics depends strongly on the underlying population distribution.

The simulated results have showed that the sample mean is less variance than the sample median. b) The graphical and analytical simulated results indicated that the shape of the sampling distribution of the statistics is approximately chi-square with n-1 degrees of freedom for small sample size and the underlying distribution is normal.

Not symmetric for small degrees of freedom. c) The simulated results showed that the sample mean and the sample variance are not correlated when the underlying population distributions are uniform or normal ; however, the simulated 37 results showed that these statistics are correlated in the exponential case.

التخصصات الرئيسية

الرياضيات

الموضوعات

• أساليب المحاكاة

عدد الصفحات

97

قائمة المحتويات

• APA
• MLA
• AMA

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-302107