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Quantile functions
Definition of quantile function:
Q(p) = min{x : F(x) >= p}, 0 < p < 1
Properties:
Special case: normal distribution
Define z_{α}
Examples
z_{0.025}, z_{0.01}, z_{0.005}
The idea
Make a table, accumulate probabilities
Example: X ~ binom
, Y = something
Introduce the formula and conditions
Intuitive formula
Example: X ~ norm
, Y = linear transformation
Fact: if X is any norm then lin. trans. is also normal
Example: X ~ norm
, Y = exp(X) (lognormal)
Introduce the method
Example: X ~ unif(0,1)
, Y = -ln(X) (exponential)
Probability Integral Transform
Why the PIT is important
Date: 2010-10-08 15:21:17 EDT
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