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Appendix C Formula Functions Reference 477
Probability Functions
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.
Figure C.13 Comparison of Normal Density and t-density
C Formula Functions Reference
normal density
t-density
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), which 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 valud, 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 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