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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.
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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 .
See also cumchi(), runi().
Gary Oehlert
2003-01-15