The Chi Squared is a continuous distribution bounded on the lower side. Note that the Chi Squared distribution is a subset of the Gamma distribution with beta=2 and alpha=nµ/2. Like the Gamma distribution, it has three distinct regions. For nµ=2, the Chi Squared distribution reduces to the Exponential distribution, starting at a finite value at minimum x and decreasing monotonically thereafter. For nµ<2, the Chi Squared distribution tends to infinity at minimum x and decreases monotonically for increasing x. For nµ>2, the Chi Squared distribution is 0 at minimum x, peaks at a value that depends on nµ, decreasing monotonically thereafter.
Because the Chi Squared distribution does not have a scaling parameter, its utilization is somewhat limited. Frequently, this distribution will try to represent data with a clustered distribution with nµ less than 2. However, it can be viewed as the distribution of the sum of squares of independent unit normal variables with nµ degrees of freedom and is used in many statistical tests.
Examples of each of the regions of the Chi Squared distribution are shown above. Note that the peak of the distribution moves away from the minimum value for increasing nu, but with a much broader distribution.
Sample (both high and low percentiles = 5)
Generates a sample of the Chi Squared distribution.
Name |
Type |
Description |
nu |
double |
the shape parameter |
min |
double |
the minimum x value |
Type |
Description |
double |
the generated sample |
Generates a sample of the Chi Squared distribution with min
set to 0. Is equivalent to chi2(nu, 0).
Name |
Type |
Description |
nu |
double |
the shape parameter |
Type |
Description |
double |
the generated sample |
Generates a sample of the Chi Squared distribution using the specified random number generator.
Name |
Type |
Description |
nu |
double |
the shape parameter |
min |
double |
the minimum x value |
r |
java.util.Random |
the random number generator |
Type |
Description |
double |
the generated sample |
This document includes content from the Stat::Fit User's Manual. Copyright © 2016 Geer Mountain Software Corp.