{"id":35,"date":"2024-04-03T23:09:24","date_gmt":"2024-04-03T20:09:24","guid":{"rendered":"https:\/\/sisu.ut.ee\/measurement\/distribution-functions-normal-gaussian-distribution\/"},"modified":"2024-06-19T16:30:05","modified_gmt":"2024-06-19T13:30:05","slug":"distribution-functions-normal-gaussian-distribution","status":"publish","type":"page","link":"https:\/\/sisu.ut.ee\/measurement\/distribution-functions-normal-gaussian-distribution\/","title":{"rendered":"3. The basic concepts and tools"},"content":{"rendered":"<p><strong>Brief summary:\u00a0<\/strong>This section presents the most basic concepts and tools for practical estimation of measurement uncertainty. First, the concepts of random quantities and distribution functions are introduced. Then the Normal distribution \u2013 the most important distribution function in measurement science \u2013 is explained and its two main parameters \u2013 the mean value and standard deviation \u2013 are introduced (3.1). Based on standard deviation the concept of standard uncertainty is introduced (3.1, 3.2). Thereafter the A type and B type uncertainty estimation is introduced (3.3). The mean value of random quantities is also a random quantity and its reliability can be described by the standard deviation of the mean (3.4). Besides the normal distribution three more distribution functions are introduced: rectangular and triangular distribution (3.5) as well as the Student distribution (3.6).<\/p>\n<ul>\n<li><a style=\"line-height: 1.6em;\" title=\"\" href=\"https:\/\/sisu.ut.ee\/measurement\/31-normal-distribution\/\">3.1. The Normal distribution<\/a><\/li>\n<li><a style=\"line-height: 1.6em;\" title=\"\" href=\"https:\/\/sisu.ut.ee\/measurement\/32-mean-standard-deviation-and-standard-uncertainty\/\">3.2. Mean, standard deviation and standard uncertainty<\/a><\/li>\n<li><a style=\"line-height: 1.6em;\" title=\"\" href=\"https:\/\/sisu.ut.ee\/measurement\/33-and-b-type-uncertainty-estimates\/\">3.3. A and B type uncertainty estimates<\/a><\/li>\n<li><a style=\"line-height: 1.6em;\" title=\"\" href=\"https:\/\/sisu.ut.ee\/measurement\/33-standard-deviation-mean\/\">3.4. Standard deviation of the mean<\/a><\/li>\n<li><a style=\"line-height: 1.6em;\" title=\"\" href=\"https:\/\/sisu.ut.ee\/measurement\/34-other-distribution-functions-rectangular-and-triangular-distribution\/\">3.5. Rectangular and triangular distribution<\/a><\/li>\n<li><a style=\"line-height: 1.6em;\" title=\"\" href=\"https:\/\/sisu.ut.ee\/measurement\/35-other-distribution-functions-student-distribution\/\">3.6. The Student distribution<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Brief summary:\u00a0This section presents the most basic concepts and tools for practical estimation of measurement uncertainty. First, the concepts of random quantities and distribution functions are introduced. Then the Normal distribution \u2013 the most important distribution function in measurement science &#8230;<\/p>\n","protected":false},"author":14,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-35","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages\/35","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/users\/14"}],"replies":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/comments?post=35"}],"version-history":[{"count":2,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages\/35\/revisions"}],"predecessor-version":[{"id":689,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages\/35\/revisions\/689"}],"wp:attachment":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/media?parent=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}