Using JMP - SAS

422 Formula Functions Reference Appendix B
Probability Functions
t Density
Accepts a quantile argument from the range of values for the t-distribution, a degrees of freedom argument,
and an optional noncentrality parameter. It returns the value of the t-density function (pdf) for the
arguments. To compare a t-density with 5 df with a standard normal distribution, you can create a column
of quantile values (x) with the formula count(-3, 3, nrow()). A second column is computed as t Density(X).
A third column is computed as Normal Density(X). Then select Graph > Overlay to plot the t-density and
the normal density by x. You will see that the t-density has slightly more spread than the normal.
t Distribution
Accepts three arguments: a quantile, a degrees of freedom, and a noncentrality parameter. It returns the
probability that an observation from the Student’s t-distribution with the specified noncentrality parameter
and degrees of freedom is less than or equal to the given quantile. For example, the expression t
Distribution(.9, 5) returns the probability that an observation from the Student’s t-distribution centered at 0
with 5 degrees of freedom is less than or equal to 0.9. The expression is evaluated as 0.79531. t-distribution
accepts integer and noninteger degrees of freedom. It is centered at 0 by default, but you can enter a value
for the noncentrality parameter. The t Quantile function is the inverse of the t Distribution function.
t Quantile
Accepts three arguments: a probability p, a degrees of freedom, and a noncentrality parameter. It returns the
p th quantile from the Student’s t-distribution with the specified noncentrality parameter and degrees of
freedom. For example, the expression Student’s t Quantile(.95, 2.5) returns the 95% quantile from the
Student’s t-distribution centered at 0 with 2.5 degrees of freedom. The expression evaluates as 2.558219.
The t Quantile function is the inverse of the t Distribution function. This function also accepts integer and
noninteger degrees of freedom. It is centered at 0 by default, but you have the option to enter a value for the
noncentrality parameter. The t Distribution function is the inverse of the t Quantile function.
Weibull Density
Accepts a quantile argument from a range of values for the Weibull distribution. It returns the value of the
Weibull probability density function (pdf). This function is the probability that an observation from a
Weibull distribution is less than or equal to the specified quantile argument.
Weibull Distribution
Uses an argument with a quantile valued, an optional value for the scale parameter α and an optional shape
parameter β. It returns the probability that an observation is less than or equal to the specified x for Weibull
distribution with the shape and scale parameters that you specified. The Weibull Distribution function is
the inverse of Weibull Quantile function.
The Weibull distribution has different shapes depending on the values of α (a scale parameter that affects
the x direction) and β (a shape parameter). It often provides a good model for estimating the length of life,
especially for mechanical devices and in biology. The two-parameter Weibull is the same as the
three-parameter Weibull with a threshold of zero.