hyperfine.distributions.modified_beta_2_cdf

hyperfine.distributions.modified_beta_2_cdf(z: Sequence[float], alpha_1: Annotated[float, slice(0, None, None)], beta_1: Annotated[float, slice(0, None, None)], z_max_1: Annotated[float, slice(0, None, None)], fraction_1: Annotated[float, slice(0, 1, None)], alpha_2: Annotated[float, slice(0, None, None)], beta_2: Annotated[float, slice(0, None, None)], z_max_2: Annotated[float, slice(0, None, None)]) → Sequence[float]

Cumulative density function for a weighted sum of two modified beta distributions.

This modified form extends the beta distribution’s domain from \(z \in [0, 1]\) to \(z \in [0, \max (z_{\mathrm{max},1}, z_{\mathrm{max},2})]\).

Parameters:

• z – Position.

• alpha_1 – First shape parameter of the first component.

• beta_1 – Second shape parameter of the first component.

• z_max_1 – Upper bounds of the domain of the first component.

• fraction_1 – Fractional weight of the first component.

• alpha_2 – First shape parameter of the second component.

• beta_2 – Second shape parameter of the second component.

• z_max_2 – Upper bounds of the domain of the second component.

Returns:

The cumulative probability density up to position z.