KnowraCauchy distributionLinked fromLinked fromThe 11 pages that link to Cauchy distribution, each with the reason it gives.All 11Broader topic 3Related 4Compared with 4Probability density functionBroader topic: Its density illustrates that a valid density need not have a finite expectation.Augustin-Louis CauchyBroader topic: The distribution’s name commemorates Cauchy’s work on probability-related mathematics.Normal distributionCompared with: Its extreme tails show why normal-based averages and uncertainty estimates can fail.Improper integralRelated: Its density integrates to one, but its expected value diverges as an improper integral.PiRelated: Its normalized density contains pi despite having no finite mean.OutlierRelated: Values far from the center can be expected, so distance alone does not establish anomaly.Gaussian functionCompared with: A similar central shape hides tails that decay far more slowly.Gaussian distributionCompared with: Its extreme tails show how dramatically Gaussian-based averaging can fail.Student's t-distributionBroader topic: With one degree of freedom, the t-distribution is exactly this distribution.Gaussian integralCompared with: Its normalization is finite, but its tails decay far more slowly than a Gaussian's.Maria Gaetana AgnesiRelated: The witch of Agnesi’s curve can serve as a scaled density shape for this distribution.