numpy.random.power

numpy.random.power(a, size=None)

Возвращает выборки из распределения степени с положительным показателем a - 1 на интервале [0, 1].

Также известно как распределение степенной функции.

Примечание

В новом коде следует использовать метод power экземпляра default_rng(); см. random-quick-start.

Параметры

afloat or array_like of floats

Параметр распределения. Должен быть неотрицательным.

sizeint or tuple of ints, optional

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

Возвращает

outndarray or scalar

Выборка из распределения с указанными параметрами.

Возбуждает

ValueError

Если a < 1.

См. также

Generator.power

который следует использовать в новом коде.

Примечания

Плотность вероятности

<img alt="P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0." 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

Распределение степенной функции — это просто обратное распределение Парето. Его также можно рассматривать как частный случай распределения бета.

Например, оно используется для моделирования завышенных сообщений об страховых претензиях.

Ссылки

1

Кристиан Кляйбер, Сэмюэл Котц, «Статистические распределения размеров в экономике и актуарных науках», Wiley, 2003.

2

Хекерт, Н. А. и Филлибен, Джеймс Дж. «Руководство NIST 148: Справочное руководство Dataplot, том 2: Подкоманды Let и библиотечные функции», Справочная серия Национального института стандартов и технологий, июнь 2003 г. https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf

Примеры

Генерация выборок из распределения:

>>> a = 5. # shape
>>> samples = 1000
>>> s = np.random.power(a, samples)

Отображение гистограммы выборок вместе с функцией плотности вероятности:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, bins=30)
>>> x = np.linspace(0, 1, 100)
>>> y = a*x**(a-1.)
>>> normed_y = samples*np.diff(bins)[0]*y
>>> plt.plot(x, normed_y)
>>> plt.show()

Сравните распределение степенной функции с обратным распределением Парето.

>>> from scipy import stats 
>>> rvs = np.random.power(5, 1000000)
>>> rvsp = np.random.pareto(5, 1000000)
>>> xx = np.linspace(0,1,100)
>>> powpdf = stats.powerlaw.pdf(xx,5)  

>>> plt.figure()
>>> plt.hist(rvs, bins=50, density=True)
>>> plt.plot(xx,powpdf,'r-')  
>>> plt.title('np.random.power(5)')

>>> plt.figure()
>>> plt.hist(1./(1.+rvsp), bins=50, density=True)
>>> plt.plot(xx,powpdf,'r-')  
>>> plt.title('inverse of 1 + np.random.pareto(5)')

>>> plt.figure()
>>> plt.hist(1./(1.+rvsp), bins=50, density=True)
>>> plt.plot(xx,powpdf,'r-')  
>>> plt.title('inverse of stats.pareto(5)')

<img alt="../../../_images/numpy-random-power-1_01_02.png" 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Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm3AuuDzRcDTm1Jahfqw6cOZHAIRiTGwGwO70pY5FWWNm