Cauchy Distribution

Introduction

First, apply the Cauchy distribution,

,

where γ = x₀ = 1, as seed to the aggregation function . Using the following cdf,

where a = b = 1, we let

Differentiate twice to find the density function of the cdf, producing

Gallery

Function f(x, y, ρ) produces the following plots at ρ = 2. The first plots the function value at the given co-ordinate points, the second plots line contours, and the third renders the contours over a colour spectrum. Notice how the plot clusters along the diagonal.

Full-size

Full-size

Full-size

The following are animations of a monotonically-increasing value of ρ = 1, ..., 20 for f(x, y, ρ).

Full-size

Full-size

Full-size

Archive

Below is a listing of available stills in EPS (full-colour and monochrome Encapsulated PostScript) for easy type-setting and PNG (full-colour Portable Network Graphics) for multimedia. They're arranged by type (three-dimensional plot, contour lines, spectral contours) and variable ρ for function f(x, y, ρ).

EPS (Encapsulated PostScript)

PNG (Portable Network Graphics)

ρ 3D Lines Spectral 1 colour | grey colour | grey colour | grey 2 colour | grey colour | grey colour | grey 3 colour | grey colour | grey colour | grey 4 colour | grey colour | grey colour | grey 5 colour | grey colour | grey colour | grey 6 colour | grey colour | grey colour | grey 7 colour | grey colour | grey colour | grey 8 colour | grey colour | grey colour | grey 9 colour | grey colour | grey colour | grey 10 colour | grey colour | grey colour | grey 11 colour | grey colour | grey colour | grey 12 colour | grey colour | grey colour | grey 13 colour | grey colour | grey colour | grey 14 colour | grey colour | grey colour | grey 15 colour | grey colour | grey colour | grey 16 colour | grey colour | grey colour | grey 17 colour | grey colour | grey colour | grey 18 colour | grey colour | grey colour | grey 19 colour | grey colour | grey colour | grey 20 colour | grey colour | grey colour | grey

3D Lines Spectral colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour colour

← Back to index. Kristaps Dzonsons, $Date: 2011/03/08 13:18:07 $