Documentation/How Tos/Calc: CHISQDIST function
CHISQDIST
Calculates values for a χ2-distribution.
Syntax
CHISQDIST(x; k; Cumulative)
- x is the number, at which you will evaluate the χ2-distribution.
- k sets the degrees of freedom for the χ2-distribution
- Constraint: k must be a positive integer
- Cumulative is a logical value.
- In the case Cumulative=TRUE() the cumulative distribution function is used, in the case Cumulative=FALSE() the probability density function. This parameter is optional. It is set to TRUE() if missing.
Semantic
CHISQDIST(x;k;FALSE()) returns values of the probability density function for the χ2-distribution:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle = \begin{cases} 0, & \textrm{if}\; x \le 0 \\ \displaystyle \frac {x^{\frac k 2 -1}\,\mathrm e^{- \frac x 2}} {2^{\frac k 2}\,\Gamma(\frac k 2) }, & \textrm{if}\; x > 0 \end{cases} }
CHISQDIST(x;k;TRUE()) returns the left tail probability for the χ2-distribution:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle = \begin{cases} 0, & \textrm{if}\; x \le 0 \\ \displaystyle \int_0^x \frac {t^{\frac k 2 -1}\,\mathrm e^{- \frac t 2}} {2^{\frac k 2}\,\Gamma(\frac k 2) }\,\mathrm d t, & \textrm{if}\; x > 0 \end{cases} }
Example
CHISQDIST(2.3;15;FALSE())
CHISQDIST(2.3;2;FALSE())
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CHISQDIST(1.5;2;TRUE())
other valid call: CHISQDIST(1.5;2) |
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CHISQDIST(18;15;TRUE())
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Remarks
If you need CHISQDIST(x;k;TRUE()) with a non integer parameter k, then use GAMMADIST(x;k/2;2) instead.
For to get the right tail for large values x, do not calculate 1 − CHISQDIST. It is less accurate in those cases than using CHIDIST. CHISQDIST(x;k;TRUE()) + CHIDIST(x;k) = 1.
In the density case the internal calculation uses logarithmic- and exponential function, if x >1425 or x · k > 1391000. The results are less accurate in those cases.
Issues
This function is not available in version 3.0 and earlier.
See Also
