Brazilian Journal of Probability and Statistics

Making the Cauchy work

Saralees Nadarajah

Full-text: Open access

Abstract

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. More than 10 practical situations where the truncated distribution could be applied are discussed. Explicit expressions are derived for the moments, L moments, mean deviations, moment generating function, characteristic function, convolution properties, Bonferroni curve, Lorenz curve, entropies, order statistics and the asymptotic distribution of the extreme order statistics. Estimation procedures are detailed by the method of moments and the method of maximum likelihood and expressions derived for the associated Fisher information matrix. Simulation issues are discussed. Finally, an application is illustrated for consumer price indices from the six major economics.

Article information

Source
Braz. J. Probab. Stat., Volume 25, Number 1 (2011), 99-120.

Dates
First available in Project Euclid: 3 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1291387776

Digital Object Identifier
doi:10.1214/09-BJPS112

Mathematical Reviews number (MathSciNet)
MR2746495

Zentralblatt MATH identifier
1298.60027

Keywords
Cauchy distribution convolution estimation moments order statistics truncated Cauchy distribution

Citation

Nadarajah, Saralees. Making the Cauchy work. Braz. J. Probab. Stat. 25 (2011), no. 1, 99--120. doi:10.1214/09-BJPS112. https://projecteuclid.org/euclid.bjps/1291387776


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