Statistics

2502 Submissions

[2] viXra:2502.0136 [pdf] replaced on 2025-03-04 07:38:31

Logarithm of Exponential and Cauchy Random Variables

Authors: Josef Bukac
Comments: 5 Pages.

We show how to calculate the expectation and the second moment of logarithm of exponential distribution. There are two ways to do this.The Cauchy distribution has no expectation but we calculate the expectation and second moment of the logaritm of the absolute value of the Cauchy distribution.
Category: Statistics

[1] viXra:2502.0097 [pdf] submitted on 2025-02-14 18:48:25

The Eggenberger-Polya Urn Process: Probabilities of Revisited Ball Ratios

Authors: Richard J. Mathar
Comments: 14 Pages.

The Eggenberger-Polya urn process starts with an urn that contains balls of two colors. At each step a ball in the urn is randomly chosen and a ball of the same color added to the urn. The probabilities of finding specified numbers of balls of the two colors later on can be visualized as a non-isotropic walk of U(p) and R(ight) steps on a square lattice. We discuss some numerical aspects of the probability that a ratio of the ball numbers of the two colors reappears later on during the process.
Category: Statistics