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Built-in Mathematica Symbol

InverseBetaRegularized

InverseBetaRegularized[s, a, b]
gives the inverse of the regularized incomplete beta function.

With the regularized incomplete beta function defined by , InverseBetaRegularized[s, a, b] is the solution for z in .

InverseBetaRegularized[z₀, s, a, b] gives the inverse of BetaRegularized[z₀, z, a, b].

Note that the arguments of InverseBetaRegularized are arranged differently than in InverseGammaRegularized.

For certain special arguments, InverseBetaRegularized automatically evaluates to exact values.

Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Series expansion at the origin:

InverseBetaRegularized threads element-wise over lists:

Evaluate the 4-argument generalized case:

Model the PDF of the beta distribution through uniformly distributed random numbers:

Compare binned modeled distribution with exact distribution:

Solve a transcendental equation:

InverseBetaRegularized evaluates numerically only for

is not automatically interpreted as an inverse regularized beta function: