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474 Formula Functions Reference Appendix C
Probability Functions
Figure C.10 Overlay Plot of Three F-Density Curves
F(20, 50)
F(5, 10)
F(10, 20)
F Distribution
Accepts four arguments: a quantile, a numerator and denominator degrees of freedom, and a
noncentrality parameter. It returns the probability that an observation from the F-distribution with the
specified noncentrality parameter and degrees of freedom is less than or equal to the given quantile. For
example, the expression F Distribution(3.32, 2, 3) returns the probability that an observation from the
central F-distribution with 2 degrees of freedom in the numerator and 3 degrees of freedom in the
denominator is less than or equal to 3.32. The expression evaluates as 0.82639.
The F-distribution function accepts integer and noninteger degrees of freedom. By default, the
non-central parameter is set to 0. The F-distribution function is the inverse of the F Quantile function.
F Quantile
Accepts four arguments: a probability p, a numerator and denominator degrees of freedom, and a
noncentrality parameter. It returns the p th quantile from the F-distribution with the specified
noncentrality parameter and degrees of freedom. For example, the expression F Quantile(0.95, 2, 10, 0)
returns the 95% quantile from the F-distribution centered at 0 with 2 degrees of freedom in the
numerator and 10 degrees of freedom in the denominator. The expression evaluates as 4.1028.
The F Quantile function accepts integer and noninteger degrees of freedom. By default, the
non-central parameter is set to 0. The F Quantile function is the inverse of the F Distribution function.
Gamma Density
Requires a quantile argument. Also accepts an optional shape parameter, which must be greater than
zero and defaults to 1. A scale parameter b, which must be greater than zero and defaults to 1 is
optional. And a threshold parameter, which must be in the range -∞ < θ < +∞ and defaults to zero is
optional. Figure C.11 shows the shape of gamma probability density functions for shape parameters of
1, 3, and 5. The standard gamma density function is strictly decreasing when α (shape) ≤1. When
α > 1 the density function begins at zero when x is θ, increases to a maximum, and then decreases.
Gamma Distribution
Is based on the standard gamma function, and accepts a single argument with a quantile value. The
shape, scale, and threshold parameters are optional, with defaults as described previously in the
discussion of the Gamma Density function. It returns the probability that an observation from a