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prefect.utilities.math

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Functions

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poisson_interval

poisson_interval(average_interval: float, lower: float = 0, upper: float = 1) -> float

Generates an “inter-arrival time” for a Poisson process.

Draws a random variable from an exponential distribution using the inverse-CDF method. Can optionally be passed a lower and upper bound between (0, 1] to clamp the potential output values.

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exponential_cdf

exponential_cdf(x: float, average_interval: float) -> float

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lower_clamp_multiple

lower_clamp_multiple(k: float) -> float

Computes a lower clamp multiple that can be used to bound a random variate drawn from an exponential distribution.

Given an upper clamp multiple k (and corresponding upper bound k * average_interval), this function computes a lower clamp multiple c (corresponding to a lower bound c * average_interval) where the probability mass between the lower bound and the median is equal to the probability mass between the median and the upper bound.

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clamped_poisson_interval

clamped_poisson_interval(average_interval: float, clamping_factor: float = 0.3) -> float

Bounds Poisson “inter-arrival times” to a range defined by the clamping factor.

The upper bound for this random variate is: average_interval * (1 + clamping_factor). A lower bound is picked so that the average interval remains approximately fixed.

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bounded_poisson_interval

bounded_poisson_interval(lower_bound: float, upper_bound: float) -> float

Bounds Poisson “inter-arrival times” to a range.

Unlike clamped_poisson_interval this does not take a target average interval. Instead, the interval is predetermined and the average is calculated as their midpoint. This allows Poisson intervals to be used in cases where a lower bound must be enforced.