A RetroSearch Logo

Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Search Query:

Showing content from https://mathworld.wolfram.com/ProbabilityDensityFunction.html below:

Probability Density Function -- from Wolfram MathWorld

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld Probability Density Function

The probability density function (PDF) of a continuous distribution is defined as the derivative of the (cumulative) distribution function ,

so

A probability function satisfies

(6)

and is constrained by the normalization condition,

Special cases are

To find the probability function in a set of transformed variables, find the Jacobian. For example, If , then

(14)

so

(15)

Similarly, if and , then

(16)

Given probability functions , , ..., , the sum distribution has probability function

(17)

where is a delta function. Similarly, the probability function for the distribution of is given by

(18)

The difference distribution has probability function

(19)

and the ratio distribution has probability function

(20)

Given the moments of a distribution (, , and the gamma statistics ), the asymptotic probability function is given by

(21)

where

(22)

is the normal distribution, and

(23)

for (with cumulants and the standard deviation; Abramowitz and Stegun 1972, p. 935).

See alsoContinuous Distribution

,

Cornish-Fisher Asymptotic Expansion

,

Discrete Distribution

,

Distribution Function

,

Joint Distribution Function

,

Ratio Distribution Explore with Wolfram|Alpha ReferencesAbramowitz, M. and Stegun, I. A. (Eds.). "Probability Functions." Ch. 26 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 925-964, 1972.Evans, M.; Hastings, N.; and Peacock, B. "Probability Density Function and Probability Function." ยง2.4 in Statistical Distributions, 3rd ed. New York: Wiley, pp. 9-11, 2000.McLaughlin, M. "Common Probability Distributions." http://www.geocities.com/~mikemclaughlin/math_stat/Dists/Compendium.html.Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, p. 94, 1984. Referenced on Wolfram|AlphaProbability Density Function Cite this as:

Weisstein, Eric W. "Probability Density Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProbabilityDensityFunction.html

Subject classifications

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4