Using JMP - SAS

Appendix B Formula Functions Reference 417
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 Scripting
Guide for details about syntax.
Beta Density
Requires three arguments: quantile argument and the shape parameters alpha and beta. A threshold
parameter (θ) and a scale parameter (σ > 0) are additional arguments. 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].
Beta Distribution
The beta distribution has two shape parameters: α > 0 and β > 0. A threshold parameter (θ) and a scale
parameter (σ) are additional arguments, where θ≤ x ≤θ + σ. The default value for θ is 0. The default value
for σ is 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 density function
(pdf) for the arguments.
ChiSquare Distribution
Accepts a response argument (range of x values) and three parameter arguments: a quantile, a degrees of
freedom, and a noncentrality parameter. It returns the probability that an observation from the Chi-squared
distribution with the specified noncentrality parameter and degrees of freedom is less than or equal to the
given quantile. For example, the expression ChiSquare Distribution(11.264, 5) returns the probability that
an observation from the Chi-squared distribution centered at 0 with 5 degrees of freedom is less than or
equal to 11.264. The expression evaluates as 0.95361.
Furthermore, the ChiSquare Distribution function accepts integer and noninteger degrees of freedom. It is
centered at 0 by default. The ChiSquare Distribution function is the inverse of the ChiSquare Quantile
function.