Probability: Uniform Distribution

Uniform Distribution

Explained:

The uniform distribution is the most simple continuous distribution in probability. It has constant probability density on an interval (a, b) and zero probability density elsewhere. The distribution is specified by two parameters: the end points a and b. We denote the distribution U(a,b). It’s probability density function (PDF) is:

[1]

which is illustrated in Exhibit 1

U(a,b) Probability Density Function
Exhibit 1

The U(a,b) distribution has constant probability density between a and b, and 0 probability density elsewhere.

A U(a,b) random variable has cumulative distribution function (CDF) and inverse CDF:

	[2]

	[3]



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The expectation, standard deviation, skewness and kurtosis of a U(a,b) random variable are:

	[4]

	[5]

	[6]

	[7]

Related Internal Links

chi-squared distribution If you square a normal random variable, the result is a chi-squared random variable.

expected value A parameter describing the "center of gravity" of a distribution.

joint normal distribution A multivariate distribution with normal marginal distributions.

kurtosis A parameter describing the peakedness and tails of a distribution.

lognormal distribution A random variable is lognormal if its logarithm is normal.

normal distribution Perhaps the most important probability distribution for probability and statistics.

quantile A notion from probability that can be used as a parameter.

skewness A parameter that describes the lack of symmetry of a distribution.

standard deviation A parameter describing the dispersion of a distribution.

uniform distribution A continuous probability distribution that has constant probability on a finite interval.

Related Books

Degroot and Schervish (2002) is a standard university text. Evans, Hastings and Peacock (2000) is a handy reference with detailed information on numerous probability distributions.

Probability and Statistics
Morris H. Degroot and Mark J. Schervish
	quality
	technical
2002

Statistical Distributions
M. Evans, N. Hastings, B. Peacock
	quality
	technical
2000