A random variable X follows a Cauchy distribution if its density function is of the form:
The parameters α and θ are the location and dispersion parameters, respectively.
The Cauchy distribution is symmetric about \( { x = \alpha } \), which represents the median. The first quartile and the third quartile are given by \( { \alpha \pm \theta } \).
The Cauchy distribution is a continuous probability distribution.
Cauchy distribution, \( { \theta=1 } \), \( { \alpha=0 } \)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
REFERENCES
Cauchy, A.L.: Sur les résultats moyens d'observations de même nature, et sur les résultats les plus probables. C.R. Acad. Sci. 37, 198–206 (1853)
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
(2008). Cauchy Distribution. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_46
Download citation
DOI: https://doi.org/10.1007/978-0-387-32833-1_46
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-31742-7
Online ISBN: 978-0-387-32833-1
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering