Description Usage Arguments Details Value Note Author(s) References See Also Examples

The first two derivatives of the incomplete gamma integral.

1 | ```
pgamma.deriv(q, shape, tmax = 100)
``` |

`q, shape` |
As in |

`tmax` |
Maximum number of iterations allowed in the computation
(per |

Write *x = q* and `shape =`

*a*.
The first and second derivatives with respect to *q* and *a*
are returned. This function is similar in spirit to
`pgamma`

;
define

*P(a,x) =
1/Gamma(a) integral_0^x t^(a-1) exp(-t) dt*

so that
*P(a, x)* is `pgamma(x, a)`

.
Currently a 6-column matrix is returned (in the future this
may change and an argument may be supplied so that only what
is required by the user is computed.)

The computations use a series expansion
for *a <= x <= 1* or
or *x < a*, else
otherwise a continued fraction expansion.
Machine overflow can occur for large values of *x*
when *x* is much greater than *a*.

The first 5 columns, running from left to right, are the derivatives
with respect to:
*x*,
*x^2*,
*a*,
*a^2*,
*xa*.
The 6th column is *P(a, x)* (but it is not as accurate
as calling `pgamma`

directly).

If convergence does not occur then try increasing the value of
`tmax`

.

Yet to do: add more arguments to give greater flexibility in the accuracy desired and to compute only quantities that are required by the user.

T. W. Yee wrote the wrapper function to the Fortran subroutine
written by R. J. Moore. The subroutine was modified to run using
double precision.
The original code came from `http://lib.stat.cmu.edu/apstat/187`

.
but this website has since become stale.

Moore, R. J. (1982).
Algorithm AS 187: Derivatives of the Incomplete Gamma Integral.
*Journal of the Royal Statistical Society, Series C*
*(Applied Statistics)*,
**31**(3), 330–335.

`pgamma.deriv.unscaled`

,
`pgamma`

.

1 2 3 4 5 6 7 8 |

```
Loading required package: stats4
Loading required package: splines
q q^2 shape shape^2 q.shape pgamma(q, shape)
[1,] 0.2706706 -0.1353353 -0.2958549 0.0004420282 0.07317926 0.5939942
[2,] 0.2685053 -0.1353181 -0.2946052 -0.0018133884 0.07473335 0.5983076
[3,] 0.2663406 -0.1352675 -0.2933336 -0.0040379197 0.07623631 0.6025863
[4,] 0.2641769 -0.1351843 -0.2920409 -0.0062311686 0.07768898 0.6068305
[5,] 0.2620148 -0.1350697 -0.2907277 -0.0083927774 0.07909219 0.6110400
[6,] 0.2598548 -0.1349246 -0.2893947 -0.0105224259 0.08044679 0.6152149
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.