Computes a Beta probability density function
with parameters α and β, with X between
A and B. The calculation is known to become difficult
for "small" values of α or β
(corrected in those cases). For large values, ~10, of the parameters,
the function tends to Gaussian, or ~6 if
α = β, with its
μ = α ⁄ (α + β) and
σ = √{α β ⁄
[(α + β)² (α + β + 1)]}
.
The function is for (α, β) =
(1, 1), uniform; (1⁄2, 1⁄2), arcsine;
(3⁄2, 3⁄2), "semicircle"; (2, 2), parabolic. Values below 1
give a bathtub form. |
