numpy.random.mtrand.RandomState.negative_binomial

method

RandomState.negative_binomial(n, p, size=None)

Выборка образцов из отрицательного биномиального распределения.

Образцы выбираются из отрицательного биномиального распределения со значениями параметров, n успехов и p вероятности успеха, где n > 0 и p находится в интервале [0, 1].

Параметры:

n : float or array_like of floats Параметр распределения, > 0. p : float or array_like of floats Параметр распределения, >= 0 и <=1. size : int or tuple of ints, optional Форма выходных данных. Если заданная форма, например, (m, n, k), то m * n * k образцов выбирается. Если размер равен None (по умолчанию), возвращается одно значение, если n и p оба являются скалярами. В противном случае выбирается np.broadcast(n, p).size образцов.

Возвращает:

out : ndarray or scalar Выбранные образцы из параметризованного отрицательного биномиального распределения, где каждый образец равен N, числу неудач, которые произошли до достижения в сумме n успехов.

Примечания

Функция массы вероятности отрицательного биномиального распределения

<img alt="P(N;n,p) = \frac{\Gamma(N+n)}{N!\Gamma(n)}p^{n}(1-p)^{N}," 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

где — количество успехов, — вероятность успеха, — количество испытаний, и

— это гамма-функция. Когда целое число.

<img alt="Γ(N+n)/N!Γ(n) = 組み合わせ(N+n-1, N)" class="math" src="data:image/svg+xml;base64,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

который является более распространённой формой этого термина в pmf. Распределение отрицательного биномиального распределения даёт вероятность N неудач при заданном количестве успехов n, при условии успеха на последней попытке.

Если вы бросаете игральную кость многократно до тех пор, пока не выпадет третья «1», то распределение вероятностей количества не «1», которые выпадают до третьей «1» — это распределение отрицательного биномиального распределения.

Ссылки

[1]	Weisstein, Eric W. «Распределение отрицательного биномиального распределения». Из MathWorld–ресурса Wolfram Web. http://mathworld.wolfram.com/NegativeBinomialDistribution.html

[2]	Википедия, «Распределение отрицательного биномиального распределения», https://en.wikipedia.org/wiki/Negative_binomial_distribution

Примеры

Получение выборок из распределения:

Пример из реальной жизни. Компания бурит разведочные нефтяные скважины, каждая со с оценённой вероятностью успеха 0,1. Какова вероятность одного успеха для каждой последующей скважины, то есть какова вероятность единичного успеха после бурения 5 скважин, 6 скважин и т.д.?

>>> s = np.random.negative_binomial(1, 0.1, 100000)
>>> for i in range(1, 11): # doctest: +SKIP
...    probability = sum(s<i) / 100000.
...    print(i, "wells drilled, probability of one success =", probability)