({{, (RefLink[RarerProbability, paclet:ref/RarerProbability])[dist,example] 
computes the probability for distribution dist to generate a sample that has a lower (RefLink[PDF, paclet:ref/PDF]) than example.}, {, (RefLink[RarerProbability, paclet:ref/RarerProbability])[dist,{(Subscript[ex, 1]),(Subscript[ex, 2]),…}]
computes the rarer probability for each (Subscript[ex, i]). }})

OpenersNotesSection(Spacer1)Details and Options

(RefLink[RarerProbability, paclet:ref/RarerProbability]) computes (RefLink[Probability, paclet:ref/Probability])[(RefLink[PDF, paclet:ref/PDF])[dist,y]<(RefLink[PDF, paclet:ref/PDF])[dist,x],y\[Distributed]dist].

(RefLink[RarerProbability, paclet:ref/RarerProbability]) can be seen as a multivariate extension of p-value used in statistics. If dist is univariate, continuous and symmetric, the rarer probability is equal to the "two-tailed" p-value.

(RefLink[RarerProbability, paclet:ref/RarerProbability]) is used to define anomalies in (RefLink[AnomalyDetection, paclet:ref/AnomalyDetection]), (RefLink[FindAnomalies, paclet:ref/FindAnomalies]) or (RefLink[DeleteAnomalies, paclet:ref/DeleteAnomalies]).

OpenersPrimaryExamplesSection(Spacer1)Examples  (2)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Compute the probability to obtain a rarer value than 3 from a normal distribution:

RarerProbability[NormalDistribution[],3]

N[%]

Learn a distribution on color data:

ld=LearnDistribution[{,,,,,,,,,}]

RarerProbability[ld,{,,,}]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[PDF, paclet:ref/PDF])  ▪  (RefLink[CDF, paclet:ref/CDF])  ▪  (RefLink[SurvivalFunction, paclet:ref/SurvivalFunction])  ▪  (RefLink[DistributionFitTest, paclet:ref/DistributionFitTest])  ▪  (RefLink[AnomalyDetectorFunction, paclet:ref/AnomalyDetectorFunction])  ▪  (RefLink[LearnedDistribution, paclet:ref/LearnedDistribution])  ▪  (RefLink[Quantile, paclet:ref/Quantile])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Statistical Distribution Functions, paclet:guide/StatisticalDistributionFunctions])}, {▪(RefLinkPlain[Machine Learning, paclet:guide/MachineLearning])}, {▪(RefLinkPlain[Random Variables, paclet:guide/RandomVariables])}})}})

({{(Spacer1), ({{(Spacer1)Related Links}, {(WebLink[DocumentationFooterIconsRelatedLinks-EIWL.png(Spacer1)An Elementary Introduction to the Wolfram Language, https://www.wolfram.com/language/elementary-introduction/22-machine-learning.html])(WebLink[: Machine Learning, https://www.wolfram.com/language/elementary-introduction/22-machine-learning.html])}})}})