绘制特定直方图(非正常)

Question

我试图将截断的正态分布与特定的a和b参数叠加在由完全相同的分布生成的样本直方图上。

我如何适应truncnorm(a，b)的pdf？

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import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
import matplotlib.mlab as mlab

from IPython.display import Math, Latex
# for displaying images
from IPython.core.display import Image
# import seaborn
import seaborn as sns
# settings for seaborn plotting style
sns.set()
# settings for seaborn plot sizes
sns.set(rc={'figure.figsize':(5,5)})

tempdist=[]

samples=100

for k in range(1,samples):
    #Probability
    #Storage temp as truncated normal
    #temperature as normal mean 55 with 5F variation
    storagetempfarenht = 57 #55
    storagetempkelvin = (storagetempfarenht + 459.67) * (5.0/9.0)
    highesttemp=storagetempfarenht + 5
    lowesttemp= storagetempfarenht -5
    sigma = ((highesttemp + 459.67) * (5.0/9.0)) - storagetempkelvin
    mu, sigma = storagetempkelvin, sigma
    lower, upper = mu-2*sigma , mu+2*sigma
    a=(lower - mu) / sigma
    b=(upper - mu) / sigma
    temp =stats.truncnorm.rvs(a, b, loc=mu, scale=sigma, size=1)
    mean, var, skew, kurt = stats.truncnorm.stats(a, b, moments='mvsk')

    tempdist.append(temp)

#Theses are the randomly generated values
tempdist=np.array(tempdist)

x = range(250,350)

ax = sns.distplot(tempdist,
                  bins=500,
                  kde=True,
                  color='r',
                  fit=stats.truncnorm,
                  hist_kws={"linewidth": 15,'alpha':1})
ax.set(xlabel='Trunc Normal Distribution', ylabel='Frequency')

Answer 1

对于truncnorm，sns.distplot的fit参数不能很好地工作，至少在数据有限的情况下不能。truncnorm.fit需要一些猜测，而distplot不知道如何提供这些猜测。

This post解释了如何手动调整truncnorm。下面的代码只绘制带有初始参数的truncnorm.pdf。要获得合适的参数，您可以使用链接帖子中的代码。

以下是一些备注：

• 许多numpy (和scipy)函数对完整数组进行操作，可以一次生成完整的数组。例如，kde生成一个带有N个samples.
• Setting的数组时会创建500个直方图柱，当只有100个samples.
• kde=True图时，这并没有什么帮助；默认情况下，这是一个高斯核的总和；distplot生成的数组越多，"linewidth": 15就越遵循数据的细节(而不是它一般的hist_kws中创建围绕15个像素宽的直方图条的直线)。这比条形图本身宽得多，导致了一个看起来很奇怪的情节。最好将行宽设置为1左右。
• 在Python中，for k in range(1,samples)运行for k in range(1,samples)-1次。这与Python从0开始的数组索引相关，而不是从1开始。

import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
import matplotlib.mlab as mlab
import seaborn as sns
sns.set()
sns.set(rc={'figure.figsize': (5, 5)})

samples = 100

storagetempfarenht = 57  # 55
storagetempkelvin = (storagetempfarenht + 459.67) * (5.0 / 9.0)
highesttemp = storagetempfarenht + 5
lowesttemp = storagetempfarenht - 5
sigma = ((highesttemp + 459.67) * (5.0 / 9.0)) - storagetempkelvin
mu, sigma = storagetempkelvin, sigma
lower, upper = mu - 2 * sigma, mu + 2 * sigma
a = (lower - mu) / sigma
b = (upper - mu) / sigma
temp = stats.truncnorm.rvs(a, b, loc=mu, scale=sigma, size=1)
# mean, var, skew, kurt = stats.truncnorm.stats(a, b, moments='mvsk')

# Theses are the randomly generated values
tempdist = stats.truncnorm.rvs(a, b, loc=mu, scale=sigma, size=samples)

ax = sns.distplot(tempdist,
                  # bins=10,  # 10 bins is the default
                  kde=True,
                  color='r',
                  # fit=stats.truncnorm, # doesn't work for truncnorm
                  hist_kws={"linewidth": 1, 'alpha': 1, 'label': 'Histogram'},
                  kde_kws={"linewidth": 2, 'alpha': 1, 'color': 'dodgerblue', 'label': 'Estimated kde'})
ax.set(xlabel='Trunc Normal Distribution', ylabel='Frequency')
x_left, x_right = ax.get_xlim()
x = np.linspace(x_left, x_right, 500)
y = stats.truncnorm.pdf(x, a, b, loc=mu, scale=sigma)
ax.plot(x, y, color='limegreen', label='Given truncnormal')
# for xi in (lower, upper):   # optionally draw vertical lines at upper and lower
#    ax.axvline(xi, linestyle=':', color='limegreen')
plt.legend()
plt.tight_layout()
plt.show()

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