Numpy随机数生成函数与常见分布函数解释

Numpy随机数

1. Numpy随机数概述

在Numpy中包含的随机数生成函数如下表所示：

函数	函数功能
rand(d0, d1, …, dn)	返回输入数组维度对应的矩阵
randn(d0, d1, …, dn)	返回输入数组维度对应服从标准正太分布的矩阵
randint(low[, high, size, dtype])	返回范围为[low, high)范围的整型随机数据
random_integers(low[, high, size])	返回[low, high]之间的随机整数
random_sample([size])	返回[0.0, 1.0)之间的浮点随机数
random([size])	从范围[0.0, 1.0)返回浮点随机数
ranf([size])	从范围[0.0, 1.0)返回浮点随机数
sample([size])	从范围[0.0, 1.0)返回浮点随机数
choice(a[, size, replace, p])	从给出的1维数组中产生其随机采样
bytes(length)	返回随机字节

2. 随机数生成示例

2.1 rand(d0, d1, …, dn)

该函数返回规定维度的随机矩阵，随机数是来源于服从[1,0)分布的采样。

示例：

np.random.rand(3, 4)
[[ 0.9453398   0.15785589  0.14297825  0.40554182]
[ 0.58353036  0.16330881  0.79096958  0.29872379]
[ 0.30474484  0.85217927  0.06831362  0.61730196]]

2.2 randn(d0, d1, …, dn)

该函数返回规定维度的随机矩阵，随机数是来源于服从(0,1)标准正太分布的采样。该函数与random.standard_normal类似，可以通过如下算式得到相应的正太分布N(mu, sigma^2)：

sigma * np.random.randn(…) + mu

示例：

np.random.randn(3, 4)
[[-2.30951289 -1.05847819 -0.06452076 -0.82147271]
[ 0.324241   -0.51254897  0.51067497  0.66082303]
[-0.0982416   0.78864197 -0.80479118  2.2884627 ]]

2.3 randint(low[, high, size, dtype])

该函数返回服从[low, high)离散均匀分布的随机数矩阵。若果high参数没有指定则范围将被限定为[0, low)

示例：

np.random.randint(0, 3, (3, 4))
[[1 0 2 0]
[0 2 0 2]
[2 2 2 1]]

2.4 random_integers(low[, high, size])

该函数与上一个函数类似，区别是返回服从[low, high]离散均匀分布的随机数矩阵。若果high参数没有指定则范围将被限定为[1, low]

示例：

np.random.random_integers(0, 3, (3, 4))
[[2 2 0 3]
[2 0 1 2]
[3 3 2 0]]

产生a与b之间的N个均匀整数：

a + (b - a) * (np.random.random_integers(N) - 1) / (N - 1.)

2.5 random_sample([size]),random([size]),ranf([size]),sample([size])

该函数返回范围为 [0.0, 1.0)的连续均值浮点数分布，若是需要产生的数范围为[a,b)，则：

(b - a) * random_sample() + a

示例：

np.random.random_sample((3, 4))
[[ 0.12439296  0.44063728  0.65585181  0.29929493]
[ 0.93312505  0.61461946  0.15346194  0.11332448]
[ 0.35118524  0.31794849  0.69337822  0.73912451]]

2.6 choice(a, size=None, replace=True, p=None)

该函数返回的是一维数组a中的抽取矩阵，若a是一个数字则一维数字便是np.arange(a)。

示例：

a = [2, 4, 6, 8, 10]
np.random.choice(a, (3, 4))
[[ 2  2  6  2]
[ 4 10  2  8]
[ 8 10  6  2]]

2.7 bytes(length)

返回随机字节

示例：

np.random.bytes(5)
l�;�

常见分布函数

1. Numpy中包含的分布函数

函数	具体分布
beta(a, b[, size])	Draw samples from a Beta distribution.
binomial(n, p[, size])	Draw samples from a binomial distribution.
chisquare(df[, size])	Draw samples from a chi-square distribution.
dirichlet(alpha[, size])	Draw samples from the Dirichlet distribution.
exponential([scale, size])	Draw samples from an exponential distribution.
f(dfnum, dfden[, size])	Draw samples from an F distribution.
gamma(shape[, scale, size])	Draw samples from a Gamma distribution.
geometric(p[, size])	Draw samples from the geometric distribution.
gumbel([loc, scale, size])	Draw samples from a Gumbel distribution.
hypergeometric(ngood, nbad, nsample[, size])	Draw samples from a Hypergeometric distribution.
laplace([loc, scale, size])	Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay).
logistic([loc, scale, size])	Draw samples from a logistic distribution.
lognormal([mean, sigma, size])	Draw samples from a log-normal distribution.
logseries(p[, size])	Draw samples from a logarithmic series distribution.
multinomial(n, pvals[, size])	Draw samples from a multinomial distribution.
multivariate_normal(mean, cov[, size, …)	Draw random samples from a multivariate normal distribution.
negative_binomial(n, p[, size])	Draw samples from a negative binomial distribution.
noncentral_chisquare(df, nonc[, size])	Draw samples from a noncentral chi-square distribution.
noncentral_f(dfnum, dfden, nonc[, size])	Draw samples from the noncentral F distribution.
normal([loc, scale, size])	Draw random samples from a normal (Gaussian) distribution.
pareto(a[, size])	Draw samples from a Pareto II or Lomax distribution with specified shape.
poisson([lam, size])	Draw samples from a Poisson distribution.
power(a[, size])	Draws samples in [0, 1] from a power distribution with positive exponent a - 1.
rayleigh([scale, size])	Draw samples from a Rayleigh distribution.
standard_cauchy([size])	Draw samples from a standard Cauchy distribution with mode = 0.
standard_exponential([size])	Draw samples from the standard exponential distribution.
standard_gamma(shape[, size])	Draw samples from a standard Gamma distribution.
standard_normal([size])	Draw samples from a standard Normal distribution(mean=0, stdev=1).
standard_t(df[, size])	Draw samples from a standard Student’s t distribution with df degrees of freedom.
triangular(left, mode, right[, size])	Draw samples from the triangular distribution over the interval [left, right].
uniform([low, high, size])	Draw samples from a uniform distribution.
vonmises(mu, kappa[, size])	Draw samples from a von Mises distribution.
wald(mean, scale[, size])	Draw samples from a Wald, or inverse Gaussian, distribution.
weibull(a[, size])	Draw samples from a Weibull distribution.
zipf(a[, size])	Draw samples from a Zipf distribution.

2. 函数使用

这里就是用最常用的高斯分布作为示例进行讲解，其它分的使用也是类似的。

mu = 50
sigma = 10.0
a = np.linspace(0, 100, 1000)
y = 1/(sigma * np.sqrt(2 * np.pi))*np.exp(-(a - mu)**2 / (2 * sigma**2))
data = np.random.normal(mu, sigma, 1000)
plt.figure()
plt.hist(data, 50, normed=True)
plt.plot(a, y, 'r-')
plt.show()