Chi-square probability density function
Y = chi2pdf(X,V)
Y = chi2pdf(X,V) computes
the chi-square pdf at each of the values in
the corresponding degrees of freedom in
be vectors, matrices, or multidimensional arrays that have the same
size, which is also the size of the output
scalar input is expanded to a constant array with the same dimensions
as the other input.
The degrees of freedom parameters in
be positive integers, and the values in
lie on the interval
The chi-square pdf for a given value x and ν degrees of freedom is
where Γ( · ) is the Gamma function.
If x is standard normal, then x2 is distributed chi-square with one degree of freedom. If x1, x2, ..., xn are n independent standard normal observations, then the sum of the squares of the x's is distributed chi-square with n degrees of freedom (and is equivalent to the gamma density function with parameters ν/2 and 2).
nu = 1:6; x = nu; y = chi2pdf(x,nu) y = 0.2420 0.1839 0.1542 0.1353 0.1220 0.1120
The mean of the chi-square distribution is the value of the
degrees of freedom parameter,
nu. The above example
shows that the probability density of the mean falls as