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Chisquare Density Function
The probability density curve of a Chisquare distribution is an asymmetric curve stretching over
the positive side of the line and having a long right tail. The form of the curve depends on the
value of a parameter known as the degree of freedom (d.f.).
The expected value of Chisquare statistic is its d.f., its variance is twice of its d.f., and its mode
is equal to (d.f. 2).
Chi square Distribution relation to Normal Distribution:
The Chisquare distribution is
related to the sampling distribution of the variance when the sample is from a normal
distribution. The sample variance is a sum of squares of standard normal variables N (0, 1).
Hence, the of square of N (0,1)
random variable
is a Chisquare with 1 d.f.
.
Notice that the Chisquare is related to Fstatistics as follows: F = Chisquare/d.f.
1
, where F has
(d.f.
1
= d.f. of the Chisquaretable, and d.f.
2
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This note was uploaded on 10/04/2011 for the course ECO 6416 taught by Professor Staff during the Spring '08 term at University of Central Florida.
 Spring '08
 Staff

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