R: Chi-Square Distribution
I. Calculating P(X > x)
If Q~Χ2(df), use the pchisq(q, df, lower.tail = FALSE) function to calculate P(Q > q).
If Q~Χ2(df), use the pchisq(q, df, lower.tail = FALSE) function to calculate P(Q > q).
Example 1:
If Q~Χ2(df = 7), use the following R code to calculate P(Q > 13).
> pchisq(13, df = 7, lower.tail = FALSE)
[1] 0.07210839
Example 2:
If Q~Χ2(df =12), use the following R code to calculate P(Q > 9).
> pchisq(9, df = 12, lower.tail = FALSE)
[1] 0.7029304
II. Given percentile, find corresponding q-value
If Q~Χ2(df =12), use the qchisq(percentile, df) function to find the q-value that corresponds with a given percentile.
Example:
If Q~Χ2(df =12), what q-value corresponds with the 75th percentile?
> qchisq(.75, df = 12)
[1] 14.8454
III. Simulating Chi-Square Random Variables
In statistics, one may finds the need to simulate random scenarios that have a Chi-Square distribution. To do this, we need to use the rchisq(n, df) function, where n represents the number of random observations you wish to observe.
Example:
Simulate 16 random variables drawn from the chi-square distribution with 7 degrees of freedom.
> rchisq(16, 7)
[1] 3.347265 5.020331 5.454771 2.754932 3.777500 12.515111 15.640380 5.803006
[9] 9.271064 6.013901 10.975353 3.197264 3.151790 2.162119 6.893636 7.417652
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