Module vickrey.functions

Functions used to approximate real data.

Functions

def comp_hyp(a, b, c, p, off)

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def comp_hyp(a, b, c, p, off):
    """Piecewise defined approximating function."""
    bs = _poly_coeffs(a, b, c, p)

    def inner_func(x):
        return (
            jnp.piecewise(
                x,
                [x < p[0], x > p[1]],
                [
                    _left_hyp(a),
                    _right_hyp(c),
                    lambda x: jnp.polyval(jnp.flip(bs), x),
                ],
            )
            + off
        )

    return inner_func

Piecewise defined approximating function.

def gennorm(x, beta, mu, sigma)

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def gennorm(x, beta, mu, sigma):
    """JAX implementation of an unscaled generalized normal pdf."""

    def pdf_unscaled(x, b):
        return jnp.exp(-(jnp.abs(x) ** b))

    y = (x - mu) / sigma
    return pdf_unscaled(y, beta) / sigma

JAX implementation of an unscaled generalized normal pdf.

def skewgennorm_fake(x, a, beta, mu, sigma)

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def skewgennorm_fake(x, a, beta, mu, sigma):
    """Function with the properties of generalized and skewed normal pdf."""
    y = (x - mu) / sigma
    gen = gennorm(y, beta, 0, 1)
    log = logistic(a * y)
    return 2 * gen * log / sigma

Function with the properties of generalized and skewed normal pdf.

def skewnorm(x, a, mu, sigma)

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def skewnorm(x, a, mu, sigma):
    """Faster function similar to an unscaled skewed norm pdf."""

    def pdf_unscaled(x):
        return 2 * jnp.exp(-(x**2)) * logistic(a * x)

    y = (x - mu) / sigma
    return pdf_unscaled(y) / sigma

Faster function similar to an unscaled skewed norm pdf.