See the Using JMP book for descriptions of most of these random functions. If the factor is categorical, then the distribution is characterized by probabilities specified for each category, with the values normalized to sum to 1.
Normal weighted is normally distributed with the given mean and standard deviation, but a special stratified and weighted sampling system is used to simulate very rare events far out into the tails of the distribution. This is a good choice when you want to measure very low defect rates accurately. See Statistical Details.
Normal truncated is a normal distribution limited by lower and upper limits. Any random realization that exceeds these limits is discarded and the next variate within the limits is chosen. This is used to simulate an inspection system where inputs that do not satisfy specification limits are discarded or sent back.
Normal censored is a normal distribution limited by lower and upper limits. Any random realization that exceeds a limit is just set to that limit, putting a density mass on the limits. This is used to simulate a re-work system where inputs that do not satisfy specification limits are reworked until they are at that limit.
Sampled means that JMP selects values at random from that column in the data table.
External means that JMP selects values at random from a column in another table. You are prompted to choose the table and column.
The Aligned check box is used for two or more Sampled or External sources. When checked, the random draws come from the same row of the table. This is useful for maintaining the correlation structure between two columns. If the Aligned option is used to associate two columns in different tables, the columns must have equal number of rows.
Distributions
Allows you to write your own expression in JMP Scripting Language (JSL) form into a field. This gives you flexibility to make up a new random distribution. For example, you could create a censored normal distribution that guaranteed nonnegative values with an expression like Max(0,RandomNormal(5,2)). In addition, character results are supported, so If(Random Uniform() < 0.2, "M", "F") works fine. After entering the expression, click the Reset button to submit the expression.
Using a Correlation Matrix