chi2pdf

Chi-square probability density function

Description

example

y = chi2pdf(x,nu) returns the probability density function (pdf) of the chi-square distribution with nu degrees of freedom, evaluated at the values in x.

Examples

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Compute the density of the observed value 2 in the chi-square distribution with 3 degrees of freedom.

y1 = chi2pdf(2,3)
y1 = 0.2076

Compute the density of the observed value 4 in the chi-square distributions with degrees of freedom 1 through 6.

y2 = chi2pdf(4,1:6)
y2 = 1×6

0.0270    0.0677    0.1080    0.1353    0.1440    0.1353

The mean of the chi-square distribution is equal to the degrees of freedom. Compute the density of the mean for the chi-square distributions with degrees of freedom 1 through 6.

nu = 1:6;
x = nu;
y3 = chi2pdf(x,nu)
y3 = 1×6

0.2420    0.1839    0.1542    0.1353    0.1220    0.1120

As the degrees of freedom increase, the density of the mean decreases.

Input Arguments

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Values at which to evaluate the pdf, specified as a nonnegative scalar value or an array of nonnegative scalar values.

• To evaluate the pdf at multiple values, specify x using an array.

• To evaluate the pdfs of multiple distributions, specify nu using an array.

If either or both of the input arguments x and nu are arrays, then the array sizes must be the same. In this case, chi2pdf expands each scalar input into a constant array of the same size as the array inputs. Each element in y is the pdf value of the distribution specified by the corresponding element in nu, evaluated at the corresponding element in x.

Example: [3 4 7 9]

Data Types: single | double

Degrees of freedom for the chi-square distribution, specified as a positive scalar value or an array of positive scalar values.

• To evaluate the pdf at multiple values, specify x using an array.

• To evaluate the pdfs of multiple distributions, specify nu using an array.

If either or both of the input arguments x and nu are arrays, then the array sizes must be the same. In this case, chi2pdf expands each scalar input into a constant array of the same size as the array inputs. Each element in y is the pdf value of the distribution specified by the corresponding element in nu, evaluated at the corresponding element in x.

Example: [9 19 49 99]

Data Types: single | double

Output Arguments

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pdf values evaluated at the values in x, returned as a scalar value or an array of scalar values. p is the same size as x and nu after any necessary scalar expansion. Each element in y is the pdf value of the distribution specified by the corresponding element in nu, evaluated at the corresponding element in x.

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Chi-Square pdf

The chi-square distribution is a one-parameter family of curves. The parameter ν is the degrees of freedom.

The pdf of the chi-square distribution is

$y=f\left(x|\nu \right)=\frac{{x}^{\left(\nu -2\right)/2}{e}^{-x/2}}{{2}^{\frac{\nu }{2}}\Gamma \left(\nu /2\right)},$

where ν is the degrees of freedom and Γ( · ) is the Gamma function.

Alternative Functionality

• chi2pdf is a function specific to the chi-square distribution. Statistics and Machine Learning Toolbox™ also offers the generic function pdf, which supports various probability distributions. To use pdf, specify the probability distribution name and its parameters. Note that the distribution-specific function chi2pdf is faster than the generic function pdf.

• Use the Probability Distribution Function app to create an interactive plot of the cumulative distribution function (cdf) or probability density function (pdf) for a probability distribution.

Version History

Introduced before R2006a