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The ChiSquared distribution is a right-skewed distribution bounded at zero. n is called the 'degrees of freedom' from its use in statistics below. Examples of the Chi Squared distribution are given below:

#### Uses

The sum of the squares of *n* unit-Normal distributions (i.e. Normal(0, 1)^2) is a Chisquared(*n*) distribution: so ChiSquared(2) = Normal(0,1)^2+Normal(0,1)^2 for example. It is this property that makes it very useful in statistics, particularly classical statistics.

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In our view, the ChiSquared tests and statistics get over-used (especially the GOF statistic) because the Normality assumption is often tenuous.

### Generation

The Chi Squared distribution is not directly available in Crystal Ball. However, because of its relationship to the Gamma distribution we can constructed a Chi Squared distribution by using the following equation:

#### Chisquared(*n*) = Gamma(0, *n*/2, 2)

#### Comments

As *n* gets large, so it is the sum of a large number of [N(0,10^2] distributions and, through Central Limit Theorem, approximates a Normal distribution itself.

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