Computational Aspects of An Asymptotic Analysis of Method of Moments Estimators of Parameters For the Binomial Distribution

In this thesis, I evaluate the confidence region of the known parameters p and m of the Binomial distribution and analyze them using descriptive statistics. This research first introduces the method of moments estimators of these parameters, p ̂_n and m ̂_n. Because p ̂_n and m ̂_n do not have mean values and variances, new, modified estimators, p ̃_n and m ̃_n, are presented for the parameters of the binomial distribution. I use the Delta method to develop the asymptotic distribution of p ̂_n, m ̂_n, p ̃_n and m ̃_n. The formulae used to calculate the confidence region are also highlighted in this thesis. These formulae allow us to draw confidence ellipses for the parameters. For the 100(1-α)% confidence region, we consider the ellipses: {(p,m)|Z ̂_2^2 (p,m)≤χ_2^2 (α)} and {(p,m)|Z ̃_2^2 (p,m)≤χ_2^2 (α)}, where χ^2 (α) is the percentile of chi-square distribution with two degrees of freedom. I evaluate the mean areas and standard deviation of areas of ellipses for the method of moments and modified estimators, and the coverage probability of the confidence region. I evaluate the descriptive statistics by examining the coefficients of skewness and kurtosis, and look at the histograms in order to check the quality of the normal approximation of the estimators.

Name thesis:degree_name

Master of Science (MSc)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2020

Author dc:creator

• Kaur, Manpreet

Advisor dc:contributor.advisor

• Volodin, Andrei

Committee member dc:contributor.committeemember

• Carnochan Naqvi, Sarah

Language dc:language.iso

en

DOI

https://doi.org/10.82465/5059

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/14412