The experiment is to select a random sample \( \bs{X} = \left(X_1, X_2, \ldots, X_n\right) \) of size \(n\) from a specified distribution and graphically test the data against a hypothesized parametric family of distributions. The following test distributions can be selected from the top list box;
The following sampling distribution can be selected from the second list box:
In each case the appropriate parameters can be varied with scrollbars.
The probability density function of the test distribution is shown in the first distribution graph. The quantiles of order \(\frac{i}{n + 1}\) for \(i \in \{1, 2, \ldots, n\}\) are also shown in this graph and are recorded in the quantile table. The probability density function of the sampling distribution is shown in the second distribution graph. Random vector \(\bs{Y} = \left(X_{(1)}, X_{(2)}, \ldots, X_{(n)}\right)\) is the sequence of order statitistics. The order statistic-quantile pairs are shown in the probability plot.