numpy.random.negative_binomial

numpy.random.negative_binomial(n, p, size=None)

Выборка образцов из отрицательного биномиального распределения.

Образцы выбираются из отрицательного биномиального распределения со заданными параметрами, n испытаний и p вероятностью успеха, где n целое число > 0, а p находится в интервале [0, 1].

Параметры:

n : int или array_like целых чисел Параметр распределения, > 0. Также принимаются значения с плавающей точкой, но они будут усечены до целых чисел. p : float или array_like чисел с плавающей точкой Параметр распределения, >= 0 и <=1. size : int или кортеж из целых чисел, необязательно Форма выходного массива. Если заданная форма, например, (m, n, k), тогда m * n * k образцов выбираются. Если size равен None (по умолчанию), возвращается одно значение, если n и p оба являются скалярами. В противном случае, выбираются np.broadcast(n, p).size образцов.

Возвращаемое значение:

out : ndarray или скаляр Выбранные образцы из параметризованного отрицательного биномиального распределения, где каждый образец равен N, количеству испытаний, необходимых для достижения n - 1 успеха, N - (n - 1) неудач и успеха на (N + n)-м испытании.

Примечания

Плотность вероятности для отрицательного биномиального распределения:

<img alt="P(N;n,p) = \binom{N+n-1}{n-1}p^{n}(1-p)^{N}," src="data:image/svg+xml;base64,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

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

количество испытаний. Распределение отрицательного биномиального распределения дает вероятность n-1 успехов и N неудач в N+n-1 испытаниях, и успех в (N+n)-ом испытании.

Если бросать игральную кость многократно до тех пор, пока не выпадет «1» в третий раз, то распределение вероятностей числа выпадений не «1» перед третьим выпадением «1» является распределением отрицательного биномиального распределения.

Ссылки

[R252]

Weisstein, Эрик В. «Распределение отрицательного бинома». Из MathWorld – Wolfram Web Resource. http://mathworld.wolfram.com/NegativeBinomialDistribution.html

[R253]

Википедия, «Распределение отрицательного бинома», http://en.wikipedia.org/wiki/Negative_binomial_distribution

Примеры

Получение выборок из распределения:

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

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