我需要在Python中实现一个类,它代表一个单变量(现在)正态分布。我的想法如下
class Norm():
def __init__(self, mu=0, sigma_sq=1):
self.mu = mu
self.sigma_sq = sigma_sq
# some initialization if necessary
def sample(self):
# generate a sample, where the probability of the value
# of the sample being generated is distributed according
# a normal distribution with a particular mean and variance
pass
N = Norm()
N.sample()
生成的样本应根据以下概率密度函数分发
我知道scipy.stats
和Numpy
提供了执行此操作的功能,但我需要了解这些功能是如何实现的。任何帮助将不胜感激,谢谢:)
答案 0 :(得分:2)
使用Box-Müller方法:
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答案 1 :(得分:1)
我最终使用了@sascha的建议。我查看了this维基百科文章和Numpy源代码,发现这个randomkit.c文件实现了函数rk_gauss
(实现了Box Muller变换),rk_double
和{{ 1}}(实现Mersenne Twister随机数生成器,模拟Box Muller变换所需的均匀分布随机变量)。
然后我从here改编了Mersenne Twister Generator并实现了Box Muller变换以模拟高斯(有关随机扭转发生器here的更多信息)。
这是我最后编写的代码:
rk_random
这非常有效,并且可以产生非常好的高斯
import numpy as np
from datetime import datetime
import matplotlib.pyplot as plt
class Distribution():
def __init__(self):
pass
def plot(self, number_of_samples=100000):
# the histogram of the data
n, bins, patches = plt.hist([self.sample() for i in range(number_of_samples)], 100, normed=1, facecolor='g', alpha=0.75)
plt.show()
def sample(self):
# dummy sample function (to be overridden)
return 1
class Uniform_distribution(Distribution):
# Create a length 624 list to store the state of the generator
MT = [0 for i in xrange(624)]
index = 0
# To get last 32 bits
bitmask_1 = (2 ** 32) - 1
# To get 32. bit
bitmask_2 = 2 ** 31
# To get last 31 bits
bitmask_3 = (2 ** 31) - 1
def __init__(self, seed):
self.initialize_generator(seed)
def initialize_generator(self, seed):
"Initialize the generator from a seed"
global MT
global bitmask_1
MT[0] = seed
for i in xrange(1,624):
MT[i] = ((1812433253 * MT[i-1]) ^ ((MT[i-1] >> 30) + i)) & bitmask_1
def generate_numbers(self):
"Generate an array of 624 untempered numbers"
global MT
for i in xrange(624):
y = (MT[i] & bitmask_2) + (MT[(i + 1 ) % 624] & bitmask_3)
MT[i] = MT[(i + 397) % 624] ^ (y >> 1)
if y % 2 != 0:
MT[i] ^= 2567483615
def sample(self):
"""
Extract a tempered pseudorandom number based on the index-th value,
calling generate_numbers() every 624 numbers
"""
global index
global MT
if index == 0:
self.generate_numbers()
y = MT[index]
y ^= y >> 11
y ^= (y << 7) & 2636928640
y ^= (y << 15) & 4022730752
y ^= y >> 18
index = (index + 1) % 624
# divide by 4294967296, which is the largest 32 bit number
# to normalize the output value to the range [0,1]
return y*1.0/4294967296
class Norm(Distribution):
def __init__(self, mu=0, sigma_sq=1):
self.mu = mu
self.sigma_sq = sigma_sq
self.uniform_distribution_1 = Uniform_distribution(datetime.now().microsecond)
self.uniform_distribution_2 = Uniform_distribution(datetime.now().microsecond)
# some initialization if necessary
def sample(self):
# generate a sample, where the value of the sample being generated
# is distributed according a normal distribution with a particular
# mean and variance
u = self.uniform_distribution_1.sample()
v = self.uniform_distribution_2.sample()
return ((self.sigma_sq**0.5)*((-2*np.log(u))**0.5)*np.cos(2*np.pi*v)) + self.mu