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# invchi()

Usage:
 ```invchi(P, df [,noncen, epsilon:eps] [,upper:T or lower:F]), P, df and noncen REAL, elements of P between 0 and 1, elements df > 0, elements of noncen >= 0, eps > 0 small. ```

Keywords: probabilities, random numbers, confidence intervals
```invchi(p,df) computes the pth quantile (100*p percent point, critical
value) of the chi squared distribution with df degrees of freedom.

invchi(p,df,Noncen [, epsilon:eps]) computes the pth quantile of
non-central chi-squared with non-centrality parameter Noncen.  The
accuracy of the inverse is controled by eps which has default value
1e-10.

The elements of p must be between 0 and 1 and the elements of df must be
positive but need not be integers.  If present, the elements of Noncen
must be non-negative.

Any of p, df or Noncen that are not scalars (single numbers) must be the
same size and shape.  Any argument that is a scalar is used to compute
all elements of the result.

invchi(p,df [,Noncen], upper:T) and invchi(p,df [,Noncen], lower:F)
compute an upper tail quantile mathematically equivalent to invchi(1 -
p, df [,Noncen]).  It may be more accurate for p very close to 1.

invchi() is the inverse of cumchi().

If alpha is small, invchi(alpha,df,upper:T) or invchi(1-alpha,df) is the
critical value for a chi-squared test of significance level alpha.

If Ssq is the sample variance from a normally distributed random sample
of size n, then (n-1)*Ssq/invchi(vector(1-alpha/2, alpha/2),n-1) is a
1-alpha confidence interval for the population variance.

invchi(runi(n),df [,Noncen]) will generate a random sample of size n
from a possibly non-central chi-squared distribution .