Because the Poisson distribution is discrete, it is sometimes useful to use the continuous normal distribution as an approximation. In doing so, determining the accuracy of the approximation is important. Some issues of interest include: knowing how the error depends on the Poisson parameter, knowing when the approximation overestimates or underestimates the distribution, bounding the magnitude of the error, and determining if the approximation can be improved. This paper addresses these issues by examining how two types of absolute error measurements are affected by variations in the Poisson parameter; changes in the relative error are also examined. Generally, the error decays much like a power function of the parameter; therefore, curve fitting is used to bound the error. Finally, variations on the approximation are examined; these variations are often more accurate than the standard approximation.
","abstract_html":"<p>Because the Poisson distribution is discrete, it is sometimes useful to use the continuous normal distribution as an approximation. In doing so, determining the accuracy of the approximation is important. Some issues of interest include: knowing how the error depends on the Poisson parameter, knowing when the approximation overestimates or underestimates the distribution, bounding the magnitude of the error, and determining if the approximation can be improved. This paper addresses these issues by examining how two types of absolute error measurements are affected by variations in the Poisson parameter; changes in the relative error are also examined. Generally, the error decays much like a power function of the parameter; therefore, curve fitting is used to bound the error. Finally, variations on the approximation are examined; these variations are often more accurate than the standard approximation.</p>","abstract_has_math":false,"creators":["Rich, Wesley Jacob"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Open Access Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["C. J. Gardiner, PhD, Chair","Bette Warren, PhD","Kenneth Shiskowski, PhD"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-01-01T08:00:00Z","date_published":"2009-01-01T08:00:00Z","updated_at":"2026-07-24T02:16:36Z","subjects":["Poisson distribution","Approximation theory","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.emich.edu/theses/262","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["C. J. Gardiner, PhD, Chair","Bette Warren, PhD","Kenneth Shiskowski, PhD"]},{"key":"dc:creator","label":"Author","values":["Rich, Wesley Jacob"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Poisson distribution","Approximation theory","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.emich.edu/theses/262"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Because the Poisson distribution is discrete, it is sometimes useful to use the continuous normal distribution as an approximation. In doing so, determining the accuracy of the approximation is important. Some issues of interest include: knowing how the error depends on the Poisson parameter, knowing when the approximation overestimates or underestimates the distribution, bounding the magnitude of the error, and determining if the approximation can be improved. This paper addresses these issues by examining how two types of absolute error measurements are affected by variations in the Poisson parameter; changes in the relative error are also examined. Generally, the error decays much like a power function of the parameter; therefore, curve fitting is used to bound the error. Finally, variations on the approximation are examined; these variations are often more accurate than the standard approximation.
"]},{"key":"dc:title","label":"Title","values":["Examining the accuracy of the normal approximation to the poisson random variable"]}]}],"canonical_facts":{"dc:contributor":["C. J. Gardiner, PhD, Chair","Bette Warren, PhD","Kenneth Shiskowski, PhD"],"dc:creator":["Rich, Wesley Jacob"],"dc:description.abstract":["Because the Poisson distribution is discrete, it is sometimes useful to use the continuous normal distribution as an approximation. In doing so, determining the accuracy of the approximation is important. Some issues of interest include: knowing how the error depends on the Poisson parameter, knowing when the approximation overestimates or underestimates the distribution, bounding the magnitude of the error, and determining if the approximation can be improved. This paper addresses these issues by examining how two types of absolute error measurements are affected by variations in the Poisson parameter; changes in the relative error are also examined. Generally, the error decays much like a power function of the parameter; therefore, curve fitting is used to bound the error. Finally, variations on the approximation are examined; these variations are often more accurate than the standard approximation.
"],"dc:identifier":["https://commons.emich.edu/theses/262"],"dc:subject":["Poisson distribution","Approximation theory","Mathematics"],"dc:title":["Examining the accuracy of the normal approximation to the poisson random variable"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Open Access Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T02:16:36Z"}