The Probability Plot Experiment

Distribution graph
Sampling Distribution graph
Test Distribution graph

Description

The experiment is to select a random sample of size $$n$$ from a specified distribution and graphically test the data against a hypothesized parametric family of distributions. The following sampling distribution can be selected from the list box:

In each case the appropriate parameters can be varied with scroll bars. Similarly, the following test distribution can be selected from a list box;

• standard normal distribution
• the uniform distribution on $$[0, 1]$$
• exponential distribution with parameter 1

The probability density function of the sampling distribution is shown in the second graph in blue, and on each update, the sample values are shown in red. The sample values are arranged in increasing order $$(x_{(1)}, x_{(2)}, \ldots, x_{(n)})$$ (these are the order statistics) and are displayed in the data table on each update. The probability density function of the test distribution is shown in blue in the third graph. The quantiles of order $$\frac{i}{n + 1}$$ for $$i \in \{1, 2, \ldots, n\}$$ are also shown in red in this graph and are recorded in the quantile table. On each update, the order statistic-quantile pairs are plotted in the first graph (this is the probability plot).