To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Logarithmic distribution

From Wikipedia, the free encyclopedia

Probability mass function
The function is only defined at integer values. The connecting lines are merely guides for the eye.
Cumulative distribution function

In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion

From this we obtain the identity

This leads directly to the probability mass function of a Log(p)-distributed random variable:

for k ≥ 1, and where 0 < p < 1. Because of the identity above, the distribution is properly normalized.

The cumulative distribution function is

where B is the incomplete beta function.

A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution, and Xi, i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log(p) distribution, then

has a negative binomial distribution. In this way, the negative binomial distribution is seen to be a compound Poisson distribution.

R. A. Fisher described the logarithmic distribution in a paper that used it to model relative species abundance.[1]

YouTube Encyclopedic

  • 1/1
    16 153
  • Lec-22 Laminar and Turbulent Flows


See also


  1. ^ Fisher, R. A.; Corbet, A. S.; Williams, C. B. (1943). "The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population" (PDF). Journal of Animal Ecology. 12 (1): 42–58. doi:10.2307/1411. JSTOR 1411. Archived from the original (PDF) on 2011-07-26.

Further reading

This page was last edited on 29 December 2020, at 15:59
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.