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  }{f(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)}
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  }{f(x)= 1/(s^a Gamma(a)) x^(a-1) e^-(x/s)}
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  for \eqn{x > 0}, \eqn{\alpha > 0}{a > 0} and \eqn{\sigma > 0}{s > 0}.
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  for \eqn{x > 0}, \eqn{\alpha > 0}{a > 0} and \eqn{\sigma > 0}{s > 0}.
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  The mean and variance are
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  The mean and variance are
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  \eqn{E(X) = \alpha\sigma}{E(X) = a*s} and
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  \eqn{E(X) = \alpha\sigma}{E(X) = a*s} and
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  \eqn{Var(X) = \alpha\sigma^2}{Var(X) = a*s^2}.
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  \eqn{Var(X) = \alpha\sigma^2}{Var(X) = a*s^2}.
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  \code{pgamma()} uses algorithm AS 239, see the references.
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}
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}
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\note{
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\note{
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  The S parametrization is via \code{shape} and \code{rate}: S has no
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  The S parametrization is via \code{shape} and \code{rate}: S has no
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  \code{scale} parameter.  Prior to 1.4.0 \R only had \code{scale}.
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  \code{scale} parameter.  Prior to 1.4.0 \R only had \code{scale}.
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  The cumulative hazard \eqn{H(t) = - \log(1 - F(t))}{H(t) = - log(1 - F(t))}
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  The cumulative hazard \eqn{H(t) = - \log(1 - F(t))}{H(t) = - log(1 - F(t))}
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  is \code{-pgamma(t, ..., lower = FALSE, log = TRUE)}.
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  is \code{-pgamma(t, ..., lower = FALSE, log = TRUE)}.
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}
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}
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\references{
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\references{
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  Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
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  Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
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  \emph{The New S Language}.
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  \emph{The New S Language}.
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  Wadsworth \& Brooks/Cole.
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  Wadsworth \& Brooks/Cole.
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  Shea, B. L. (1988)
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  Algorithm AS 239,  Chi-squared and Incomplete Gamma Integral,
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  \emph{Applied Statistics (JRSS C)} \bold{37}, 466--473.
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}
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}
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\seealso{
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\seealso{
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  \code{\link{gamma}} for the Gamma function, \code{\link{dbeta}} for
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  \code{\link{gamma}} for the Gamma function, \code{\link{dbeta}} for
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  the Beta distribution and \code{\link{dchisq}} for the chi-squared
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  the Beta distribution and \code{\link{dchisq}} for the chi-squared
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  distribution which is a special case of the Gamma distribution.
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  distribution which is a special case of the Gamma distribution.