{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/14412"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/14412","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Computational Aspects of An Asymptotic Analysis of Method of Moments Estimators of Parameters For the Binomial Distribution","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Kaur, Manpreet"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Science (MSc)","degree_level":"Master's","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":[],"advisors":["Volodin, Andrei"],"committee_chairs":[],"committee_members":["Carnochan Naqvi, Sarah"],"year":2020,"date_issued":"2020-09","date_published":"2020-09","updated_at":"2026-07-24T04:03:49Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/5059"],"render_values":[{"text":"https://doi.org/10.82465/5059","href":"https://doi.org/10.82465/5059","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/14412","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Volodin, Andrei"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Carnochan Naqvi, Sarah"]},{"key":"dc:creator","label":"Author","values":["Kaur, Manpreet"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-09-23T22:11:28Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-09-23T22:11:28Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-09"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/5059"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/14412"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. xii, 109 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Computational Aspects of An Asymptotic Analysis of Method of Moments Estimators of Parameters For the Binomial Distribution"]}]}],"canonical_facts":{"dc:contributor.advisor":["Volodin, Andrei"],"dc:contributor.committeemember":["Carnochan Naqvi, Sarah"],"dc:creator":["Kaur, Manpreet"],"dc:date.accessioned":["2021-09-23T22:11:28Z"],"dc:date.available":["2021-09-23T22:11:28Z"],"dc:date.issued":["2020-09"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. xii, 109 p."],"dc:description.abstract":["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."],"dc:identifier.doi":["https://doi.org/10.82465/5059"],"dc:identifier.uri":["https://hdl.handle.net/10294/14412"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Computational Aspects of An Asymptotic Analysis of Method of Moments Estimators of Parameters For the Binomial Distribution"],"dc:type":["master thesis"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:49Z"}