使用numpy生成离散概率分布

Question

我在看一个代码示例，地址是http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html#subclassing-rv-discrete，这个示例是用来实现一个生成离散值的随机数生成器，基于正态分布。这个示例（也不意外）运行得很好，但当我修改它，只允许生成左尾或右尾的结果时，发现0附近的分布太低了（0这个区间应该包含更多的值）。我可能碰到了某个边界条件，但我搞不清楚。是不是我漏掉了什么？

这是每个区间内随机数的计数结果：

np.bincount(rvs) [1082 2069 1833 1533 1199  837  644  376  218  111   55   20   12    7    2 2]

这是生成的直方图：

from scipy import stats

np.random.seed(42)

def draw_discrete_gaussian(rng, tail='both'):
    # number of integer support points of the distribution minus 1
    npoints = rng if tail == 'both' else rng * 2
    npointsh = npoints / 2
    npointsf = float(npoints)
    # bounds for the truncated normal
    nbound = 4
    # actual bounds of truncated normal
    normbound = (1+1/npointsf) * nbound
    # integer grid
    grid = np.arange(-npointsh, npointsh+2, 1)
    # bin limits for the truncnorm
    gridlimitsnorm = (grid-0.5) / npointsh * nbound
    # used later in the analysis
    gridlimits = grid - 0.5
    grid = grid[:-1]
    probs = np.diff(stats.truncnorm.cdf(gridlimitsnorm, -normbound, normbound))
    gridint = grid

    normdiscrete = stats.rv_discrete(values=(gridint, np.round(probs, decimals=7)), name='normdiscrete')
    # print 'mean = %6.4f, variance = %6.4f, skew = %6.4f, kurtosis = %6.4f'% normdiscrete.stats(moments =  'mvsk')
    rnd_val = normdiscrete.rvs()
    if tail == 'both':
        return rnd_val
    if tail == 'left':
        return -abs(rnd_val)
    elif tail == 'right':
        return abs(rnd_val)


rng = 15
tail = 'right'
rvs = [draw_discrete_gaussian(rng, tail=tail) for i in xrange(10000)]

if tail == 'both':
    rng_min = rng / -2.0
    rng_max = rng / 2.0
elif tail == 'left':
    rng_min = -rng
    rng_max = 0
elif tail == 'right':
    rng_min = 0
    rng_max = rng

gridlimits = np.arange(rng_min-.5, rng_max+1.5, 1)
print gridlimits
f, l = np.histogram(rvs, bins=gridlimits)

# cheap way of creating histogram
import matplotlib.pyplot as plt
%matplotlib inline

bins, edges = f, l
left,right = edges[:-1],edges[1:]
X = np.array([left, right]).T.flatten()
Y = np.array([bins, bins]).T.flatten()

# print 'rvs', rvs
print 'np.bincount(rvs)', np.bincount(rvs)

plt.plot(X,Y)
plt.show()

Answer 1

我根据@user333700和@user235711的评论，尝试回答我自己的问题：

我在normdiscrete = ...之前插入了一些内容

if tail == 'right':
    gridint = gridint[npointsh:]
    probs = probs[npointsh:]
    s = probs.sum()
    probs = probs / s
elif tail == 'left':
    gridint = gridint[0: npointsh]
    probs = probs[0: npointsh]
    s = probs.sum()
    probs = probs / s

生成的直方图和看起来好多了：