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The Entropy of Cauchy Distribution

The Entropy of Cauchy Distribution
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A truncated Cauchy distribution

International Journal of Mathematical Education in Science and Technology, 2006
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. One such situation in finance is discussed. Explicit expressions for the moments of the truncated distribution are also derived.
Saralees Nadarajah, Samuel Kotz
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Matrix variate Cauchy distribution

Statistics, 2003
In this article we introduce the matrix variate Cauchy distribution. Its density function has been derived using independent random matrices having dependent normal entries. Some properties of this distribution are also studied.
Rajesh R. Bandekar, Daya K. Nagar
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The skew-Cauchy distribution

Statistics & Probability Letters, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arnold, Barry C., Beaver, Robert J.
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Generalized cauchy distributions

Annals of the Institute of Statistical Mathematics, 1957
Statistical distributions of the form C(l + [' x | )~ are considered. For k = 2, m = 1 this is the Cauchy distribution. For k = 2, m == ^(n -\1), % == n~&, it is the Student-Fisher distribution with n degrees of freedom. The Cauchy distribution is of interest because the variance of the mean is infinite while that of the median is finite. In this paper
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Distributive Cauchy lattices

Algebra Universalis, 1984
The author has pioneered the study of completions of lattice ordered groups by means of Cauchy structures. This paper extends this study to arbitrary distributive lattices by means of Cauchy structures obtained from two intrinsic (and generally non-topological) lattice convergences called \(\alpha\) and \(\beta\).
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Sprays and Cauchy's Distribution

Mathematics Magazine, 1960
Thus exactly the same distribution results as if the particles had been projected from a point source at the origin. This has an application in spraying. Consider two sprays of the common revolving nozzle type, mounted so that the centres of revolution may be considered coincident, with the nozzles revolving in opposite directions and emitting thin ...
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Centered distributions with cauchy conditionals

Communications in Statistics - Theory and Methods, 1991
We introduce a bivariate distribution with Cauchy conditionals that is centered at the origin. The construction is patterned after the functional equation methods employed by Castillo and Galambos(1987), Arnold(1987), Castillo and Galambos(1989), and Arnold and Strauss( 1988a) in the development of various bivariate densities with conditionally ...
Dale N. Anderson, Barry C. Arnold
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SOME CHARACTERIZATIONS OF THE CAUCHY DISTRIBUTION

Australian Journal of Statistics, 1979
SummaryIf X and Y are independent standard Cauchy random variables then (i) Y and (X+Y)/(1‐Xu) are independent, (ii) X and (X + Y)/(1 ‐XU) are identically distributed, and (iii) X and 2X/(1‐X2) are identically distributed. Each of these three properties is shown to characterize the Cauchy distribution among absolutely continuous distributions.
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Half-Cauchy and Power Cauchy Distributions: Ordinary Differential Equations

2018
In this chapter, homogenous ordinary differential equations (ODES) of different orders were obtained for the probability density function, quantile function, survival function inverse survival function, hazard function and reversed hazard functions of half-Cauchy and power Cauchy distributions.
Hilary I. Okagbue, Muminu O. Adamu, Patience I. Adamu, Sheila A. Bishop, Ezinne C. Erondu   +4 more
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