Chi Distribution
المؤلف:
Evans, M.; Hastings, N.; and Peacock, B.
المصدر:
"Chi Distribution." §8.3 in Statistical Distributions, 3rd ed. New York: Wiley
الجزء والصفحة:
...
3-4-2021
1843
Chi Distribution
The chi distribution with 
degrees of freedom is the distribution followed by the square root of a chi-squared random variable. For 
, the 
distribution is a half-normal distribution with 
. For 
, it is a Rayleigh distribution with 
. The chi distribution is implemented in the Wolfram Language as ChiDistribution[n].
The probability density function and distribution function for this distribution are
where 
is a regularized gamma function.
The 
th raw moment is
 |
(3)
|
(Johnson et al. 1994, p. 421; Evans et al. 2000, p. 57; typo corrected), giving the first few as
The mean, variance, skewness, and kurtosis excess are given by
REFERENCES:
Evans, M.; Hastings, N.; and Peacock, B. "Chi Distribution." §8.3 in Statistical Distributions, 3rd ed. New York: Wiley, p. 57, 2000.
Johnson, N.; Kotz, S.; and Balakrishnan, N. Continuous Univariate Distributions, Vol. 1, 2nd ed. Boston, MA: Houghton Mifflin, 1994.
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