TITLE(NChisquare @@ The Non-Central Chi-Square Distribution)
USAGE(
dnchisq(x, df, lambda)
pnchisq(q, df, lambda)
qnchisq(p, df, lambda)
rnchisq(n, df, lambda)
)
ALIAS(dnchisq)
ALIAS(pnchisq)
ALIAS(qnchisq)
ALIAS(rnchisq)
DESCRIPTION(
These functions provide information about the non-central chi-square
distribution with LANG(df) degrees of freedom and non-centrality
parameter LANG(lambda).  LANG(dnchisq) gives the density, LANG(pnchisq)
gives the distribution function LANG(qnchisq) gives the quantile
function and LANG(rnchisq) generates random deviates.
PARA
The non-central chi-square distribution with EQN(df) degrees of freedom
and non-centrality parameter EQN(greeklambda) has density
DEQN(f(x) = SUP(e @@ -\lambda / 2)
  \sum_{r=0}^\infty \frac{\lambda^r}{2^r r!} \mathrm{pchisq}(x, df + 2r) 
  @@
  f(x) = exp(-lambda/2) SUM_{r=0}^infty (lambda^r / 2^r r!)
  pchisq(x, df + 2r)
)
for EQN(x GE 0).
)
SEEALSO(
LANG(LINK(dchisq)), LANG(LINK(dgamma)).
)
EXAMPLES(
pnchisq(1, df=3, lambda=0) == pchisq(1, df=3)
pnchisq(1, df=3, lambda=0:4)
)
KEYWORD(distribution)
