Description Usage Arguments Details Value References See Also Examples
Computes the incomplete gamma function and its first and second derivatives with respect to 'shape' parameter.
1 | pgamma.deriv(x, shape, scale, deriv = 0:2)
|
x |
a numeric argument, |
shape, scale |
shape and scale parameters, must be positive. |
deriv |
integer vector, order of the required derivatives. |
The regularized (standard) incomplete gamma function is given by
P(a, x) = \frac{1}{Γ(a)} \int_0^x t^{a - 1}\,e^{-t}\,dt,
which is related with the CDF of Gamma distribution (see pgamma
).
pgamma.deriv
is a C translation of the original Fortran AS 187 subroutine
by R.J. Moore.
Function pgamma.deriv
returns the value, first and second derivatives of
the regularized incomplete gamma gamma function with respect to 'shape' parameter.
Abramowitz, M., and Stegun, I.A. (1970). Handbook of Mathematical Functions. Dover, New York.
Moore, R.J. (1982). Algorithm AS 187: Derivatives of the incomplete gamma integral. Applied Statistics 31, 330-335.
1 2 3 4 5 | x <- 3
pgamma.deriv(x, 1, 1, deriv = 0:2)
# only to check 1st element
pgamma(x, 1, 1)
|
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