RarerProbability[dist,example]
computes the probability for distribution dist to generate a sample that has a lower or equal PDF than example.
RarerProbability[dist,{ex1,ex2,…}]
computes the rarer probability for each exi.


RarerProbability
RarerProbability[dist,example]
computes the probability for distribution dist to generate a sample that has a lower or equal PDF than example.
RarerProbability[dist,{ex1,ex2,…}]
computes the rarer probability for each exi.
Details and Options

- RarerProbability is a statistical function used to quantify how unusual or anomalous a given observation is within a probability distribution.
- Typical application includes identifying outliers, anomalies and statistically significant deviations from expected patterns in data analysis and machine learning workflows.
- RarerProbability[dist,x] computes Probability[PDF[dist,y]≤PDF[dist,x],ydist].
- RarerProbability can be seen as a multivariate extension of the p-value used in statistics. If dist is univariate, continuous and symmetric, the rarer probability is equal to the "two-tailed" p-value.
- RarerProbability is used to define anomalies in AnomalyDetection, FindAnomalies or DeleteAnomalies.
Related Guides
History
Text
Wolfram Research (2019), RarerProbability, Wolfram Language function, https://reference.wolfram.com/language/ref/RarerProbability.html.
CMS
Wolfram Language. 2019. "RarerProbability." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RarerProbability.html.
APA
Wolfram Language. (2019). RarerProbability. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RarerProbability.html
BibTeX
@misc{reference.wolfram_2025_rarerprobability, author="Wolfram Research", title="{RarerProbability}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/RarerProbability.html}", note=[Accessed: 08-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_rarerprobability, organization={Wolfram Research}, title={RarerProbability}, year={2019}, url={https://reference.wolfram.com/language/ref/RarerProbability.html}, note=[Accessed: 08-August-2025]}