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472 Formula Functions Reference Appendix C
Probability Functions
Probability Functions
You can create a formula that calculates probabilities and quantiles for statistical distributions like beta,
Chi-square, F, gamma, normal, Student’s t, Weibull distributions, Tukey HSD, and so on. See the JMP
Scripting Guide for details about syntax.
Beta Density
Requires three arguments: quantile argument, shape parameters alpha and beta. A threshold parameter
(theta) and a scale parameter (sigma > 0) are additional options. It returns the value of the beta
probability density function (pdf) for the given arguments. The beta density is useful for modeling the
probabilistic behavior of random variables such as proportions constrained to fall in the interval [0, 1].
Examples of densities for several combinations of α and β are shown in Figure C.8.
Figure C.8 Overlay Plot of Three Beta Density Curves
Beta Distribution
Has a positive density only for an x interval of finite length, unlike normal and gamma which have
positive density over an infinite interval. The theoretical beta distribution has a shape parameter, α > 0
and a scale parameter, β > 0, and constants a ≤ x ≤ b that define the interval for which the distribution
has values. The beta distribution function accepts the response variable argument x, whose range
defines the interval for the distribution. The standard beta distribution occurs in the interval [0, 1].
The beta distribution function is the inverse of the beta quantile function.
Beta Quantile
Accepts a probability argument, p, and shape and scale parameters, α > 0 and β > 0. It returns the p th
quantile from the standard beta distribution. The beta quantile function is the inverse of the beta
distribution function.
ChiSquare Density
Accepts a quantile argument from the range of values for the Chi-squared distribution, a degrees of
freedom argument, and an optional noncentrality parameter. It returns the value of the Chi-squared