Numpy随机数生成函数与常见分布函数解释

Myth丶恋晨 2022-05-31 10:06 234阅读 0赞

# 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：

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

## 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 ##

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

## 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()

![这里写图片描述][SouthEast]

[SouthEast]: /images/20220531/eb07a88eebcd4555b47982593f6c56c3.png