InverseBetaRegularized

InverseBetaRegularized[s,a,b]

gives the inverse of the regularized incomplete beta function.

Details

Examples

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Basic Examples  (2)

Evaluate numerically:

Plot over a subset of the reals:

Scope  (11)

Numerical Evaluation  (3)

Evaluate numerically:

Evaluate to high precision:

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

Evaluate efficiently at high precision:

Specific Values  (4)

Values of InverseBetaRegularized at fixed points:

Values at zero:

Find a value of z for which the InverseBetaRegularized[z,1,2]=0.5:

TraditionalForm formatting:

Visualization  (2)

Plot the InverseBetaRegularized function for different values of parameter a:

Plot the InverseBetaRegularized function for different values of parameter b:

Differentiation  (2)

First derivative with respect to s when a=2 and b=3:

First derivative with respect to a when b=2:

First derivative with respect to b when a=2:

Higher derivatives with respect to s when a=2 and b=3:

Plot the higher derivatives with respect to s when a=2 and b=3:

Generalizations & Extensions  (2)

InverseBetaRegularized threads elementwise over lists:

Evaluate the 4-argument generalized case:

Applications  (1)

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

Compare binned modeled distribution with exact distribution:

Properties & Relations  (2)

InverseBetaRegularized is the inverse of BetaRegularized:

Solve a transcendental equation:

Possible Issues  (2)

InverseBetaRegularized evaluates numerically only for :

In TraditionalForm, is not automatically interpreted as an inverse regularized beta function:

Introduced in 1996
 (3.0)