Chidf

Purpose

Chi-squared distribution.

Synopsis

prob = chidf(function,x,a)

Description

Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Chi-sqared distribution.

The chi-squared distribution usually models data that are positive (such as the sum of physical measurements). With integer degrees of freedom parameter v, it is equal to the sum of v normally distributed variates. This toolbox does not require that the degrees of freedom be integral and will ignore negative values in a sample. Chi-squared distributions have variance equal to twice the mean.

$f(x)={\frac {x^{\left(a-2\right)/2}\,exp\left(-x/2\right)}{2^{a/2}\,\Gamma \left(a/2\right)}}$

Inputs

• function = [ {'cumulative'} | 'density' | 'quantile' | 'random' ], defines the functionality to be used. Note that the function recognizes the first letter of each string so that the string could be: [ 'c' | 'd' | 'q' | 'r' ].

• x = matrix in which the sample data is stored, in the interval (0,inf).

for function=quantile - matrix with values in the interval (0,1).

for function=random - vector indicating the size of the random matrix to create.

• a = degrees of freedom parameter (positive integer).

Note: If inputs (x, a, and b) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function.

Note: Functions will typically allow input values outside of the acceptable range to be passed but such values will return NaN in the results.

Examples

Cumulative

>> prob = chidf('c',[3.7942 4.6052],2)
prob =
    0.8500    0.9000
>> x = 0:0.1:8;
>> plot(x,chidf('c',x,2),'b',x,chidf('c',x,0.5),'r')

Density

>> prob = chidf('d',[3.7942 4.6052],2)
prob =
    0.0750    0.0500
>> x = 0:0.1:8;
>> plot(x,chidf('d',x,2),'b',x,chidf('d',x,0.5),'r')

Quantile

>> prob = chidf('q',[0.85 0.9],2)
prob =
     3.7942    4.6052

Random

>> prob = chidf('r',[4 1],2)
prob =
    0.1023
    2.9295
    0.9990
    1.4432

See Also

betadr, cauchydf, expdf, gammadf, gumbeldf, laplacedf, logisdf, lognormdf, normdf, paretodf, raydf, triangledf, unifdf, weibulldf