numpy.random.Generator.poisson

метод

Generator.poisson(lam=1.0, size=None)

Генерирует выборки из распределения Пуассона.

Распределение Пуассона является пределом биномиального распределения при больших N.

Параметры

lamfloat or array_like of floats

Математическое ожидание интервала, должно быть >= 0. Последовательность значений математического ожидания интервала должна быть согласуема по размеру с требуемым размером.

sizeint or tuple of ints, optional

Форма выходных данных. Если заданная форма, например, (m, n, k), то m * n * k выборок генерируется. Если размер равен None (по умолчанию), возвращается единственное значение, если lam является скаляром. В противном случае, генерируется np.array(lam).size выборок.

Возвращает

outndarray or scalar

Сгенерированные выборки из распределения Пуассона с заданными параметрами.

Примечания

Распределение Пуассона

<img alt="f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!}" 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

Для событий с ожидаемым разрывом распределении Пуассона описывает вероятность

события, происходящие в наблюдаемом интервале .

Так как вывод ограничен диапазоном типа C int64, при lam значение, находящееся в пределах 10 сигм от максимального представимого значения, возникает исключение ValueError.

Ссылки

1

Weisstein, Eric W. «Распределение Пуассона». Из MathWorld – Wolfram Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html

2

Википедия, «Распределение Пуассона», https://en.wikipedia.org/wiki/Poisson_distribution

Примеры

Генерация выборок из распределения:

>>> import numpy as np
>>> rng = np.random.default_rng()
>>> s = rng.poisson(5, 10000)

Отображение гистограммы выборки:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 14, density=True)
>>> plt.show()

Сгенерировать по 100 значений для лямбда 100 и 500:

>>> s = rng.poisson(lam=(100., 500.), size=(100, 2))