- If
*X*is a random variable with cdf*F*, then the*q*-quantile of*X*is the value such that for . - When has an inverse, we write
- Now we discuss how to use Q-Q plots to draw distributions.
- Let
be a sample data from
*X*. - Re-order the s as s such that
.
- The q-q plot is based on the fact that is an
estimate of the
*(j-1/2)/n*quantile of*X*, that is,

where*F*is the distribution function under the consideration that fits the samples. - Plot against . If the distribution fits, the line would form a straight line. Use the measurement of deviation to decide whether or not the set of samples fit the distribution function.

- Let
be a sample data from
- Example 10.4 on page 365.

Meng Xiannong 2002-10-18