Essays/Chi Squared CDF

The CDF of the $\chi ^{2}$ distribution can be computed as follows.

gamma   =: ! & <:
ig0     =: 4 : '(1 H. (1+x) % x&((* ^) * (^ -)~)) y'
incgam  =: ig0 % gamma@[  NB. incomplete gamma
chisqcdf=: incgam&-:

The following examples compare calculated results against values from the Handbook of Mathematical Functions by Abramowitz and Stegun, Table 26.8.

   t26d8a=: 0.411740 0.554300 0.831211 1.145476  16.7496 20.515 22.105 25.745
   5 chisqcdf t26d8a
0.00499995 0.0100001 0.025 0.05 0.995 0.999 0.9995 0.9999

   t26d8b=: 15.137 18.421 21.108 23.513 25.745 27.856 29.877 31.828 33.720 35.564
   (1+i.10) chisqcdf t26d8b
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

---

See also

• Chi Squared CDF
• Normal CDF
• Pi (Chudnovsky Algorithm)
• Sine
• Square Root
• t-Distribution CDF
• Extended Precision Functions

---

Contributed by Roger Hui. The verb definitions are from Ewart Shaw, Hypergeometric Functions and CDFs in J, Vector, Volume 18, Number 4, April 2002.