\"This dissertation is presented in publication form and consists of two articles. The first article considers inferential procedures on the shape parameter of a gamma distribution from censored sampling. Moments for the statistic T = log(x̅r/x͠r) are found and used to derive a two-moment chi-square approximation for T. This approximation is then used for testing, estimating, and setting confidence bounds on the shape parameter of a gamma distribution. The second article concerns the Cramér-Rao lower bounds for the variances of estimators, where the estimators are based on censored data. Convenient techniques are derived to evaluate the lower bounds in the presence or absence of nuisance parameters\"--Abstract, page iii.
","abstract_html":"<p>"This dissertation is presented in publication form and consists of two articles. The first article considers inferential procedures on the shape parameter of a gamma distribution from censored sampling. Moments for the statistic T = log(x̅<sub>r</sub>/x͠<sub>r</sub>) are found and used to derive a two-moment chi-square approximation for T. This approximation is then used for testing, estimating, and setting confidence bounds on the shape parameter of a gamma distribution. The second article concerns the Cramér-Rao lower bounds for the variances of estimators, where the estimators are based on censored data. Convenient techniques are derived to evaluate the lower bounds in the presence or absence of nuisance parameters"--Abstract, page iii.</p>","abstract_has_math":false,"creators":["Wyckoff, James"],"institution":"University of Missouri--Rolla","degree_name":"Ph. D. in Mathematics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:19:21Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/325","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Wyckoff, James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Mathematics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Rolla"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/325"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"This dissertation is presented in publication form and consists of two articles. The first article considers inferential procedures on the shape parameter of a gamma distribution from censored sampling. Moments for the statistic T = log(x̅r/x͠r) are found and used to derive a two-moment chi-square approximation for T. This approximation is then used for testing, estimating, and setting confidence bounds on the shape parameter of a gamma distribution. The second article concerns the Cramér-Rao lower bounds for the variances of estimators, where the estimators are based on censored data. Convenient techniques are derived to evaluate the lower bounds in the presence or absence of nuisance parameters\"--Abstract, page iii.
"]},{"key":"dc:title","label":"Title","values":["Inferences on the shape parameter of the gamma distribution and Cramer-Rao lower bounds from censored data"]}]}],"canonical_facts":{"dc:creator":["Wyckoff, James"],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["\"This dissertation is presented in publication form and consists of two articles. The first article considers inferential procedures on the shape parameter of a gamma distribution from censored sampling. Moments for the statistic T = log(x̅r/x͠r) are found and used to derive a two-moment chi-square approximation for T. This approximation is then used for testing, estimating, and setting confidence bounds on the shape parameter of a gamma distribution. The second article concerns the Cramér-Rao lower bounds for the variances of estimators, where the estimators are based on censored data. Convenient techniques are derived to evaluate the lower bounds in the presence or absence of nuisance parameters\"--Abstract, page iii.
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