拟合对数正态分布（Python图）

Carmen González 发表于 Dev

卡门·冈萨雷斯（Carmen Gonzalez）

我试图将对数正态分布拟合到直方图数据。我试图在Stack Exchange上关注其他问题的示例，但是我不适应，因为在这种情况下，我的轴断了。我已经在该图上放置了折断的轴，我试图防止数字在轴上重叠，我从重复的轴上删除了数字，减小了第二个子图的大小，但是我无法拟合对数-普通的。如何拟合该数据集的对数正态分布？

代码：

#amostra 17B (menor intervalo)
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import lognorm
import matplotlib.ticker as tkr
import scipy, pylab
import locale
import matplotlib.gridspec as gridspec
from scipy.stats import lognorm
locale.setlocale(locale.LC_NUMERIC, "de_DE")
plt.rcParams['axes.formatter.use_locale'] = True

frequencia_relativa=[0.000, 0.000, 0.038, 0.097, 0.091, 0.118, 0.070, 0.124, 0.097, 0.059, 0.059, 0.048, 0.054, 0.043, 
                     0.032, 0.005, 0.027, 0.016, 0.005, 0.000, 0.005, 0.000, 0.005, 0.000, 0.000, 0.000, 0.000, 0.000, 
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.000, 0.000]
x=[0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 1.10, 1.20, 1.30, 1.40, 
   1.50, 1.60, 1.70, 1.80, 1.90, 2.00, 2.10, 2.20, 2.30, 2.40, 2.50, 2.60, 2.70, 2.80, 
   2.90, 3.00, 3.10, 3.20, 3.30, 3.40, 3.50, 3.60, 3.70, 3.80, 3.90, 4.00, 4.10, 4.20,
   4.30, 4.40, 4.50, 4.60, 4.70, 4.80, 4.90, 5.00, 5.10, 5.20, 5.30, 5.40, 5.50, 5.60,
   5.70, 5.80, 5.90, 6.00, 6.10, 6.20, 6.30, 6.40, 6.50, 6.60, 6.70, 6.80, 6.90, 7.00,
   7.10, 7.20, 7.30, 7.40, 7.50, 7.60, 7.70, 7.80, 7.90, 8.00]
plt.rcParams["figure.figsize"] = [20,8]
f, (ax,ax2) = plt.subplots(1,2, sharex=True, sharey=True, facecolor='w')
axes = f.add_subplot(111, frameon=False)
ax.spines['top'].set_color('none')
ax2.spines['top'].set_color('none')
gs = gridspec.GridSpec(1,2,width_ratios=[3,1])
ax = plt.subplot(gs[0])
ax2 = plt.subplot(gs[1])
ax.yaxis.tick_left()
ax.xaxis.tick_bottom()
ax2.xaxis.tick_bottom()
ax.tick_params(labeltop='off') # don't put tick labels at the top
ax2.yaxis.tick_right()
ax.bar(x, height=frequencia_relativa, alpha=0.5, width=0.1, align='edge', edgecolor='black', hatch="///")
ax2.bar(x, height=frequencia_relativa, alpha=0.5, width=0.1, align='edge', edgecolor='black', hatch="///")
ax.tick_params(axis = 'both', which = 'major', labelsize = 18)
ax.tick_params(axis = 'both', which = 'minor', labelsize = 18)
ax2.tick_params(axis = 'both', which = 'major', labelsize = 18)
ax2.tick_params(axis = 'both', which = 'minor', labelsize = 18)
ax2.xaxis.set_ticks(np.arange(7.0, 8.5, 0.5))
ax2.xaxis.set_major_formatter(tkr.FormatStrFormatter('%0.1f'))
plt.subplots_adjust(wspace=0.04)
ax.set_xlim(0,2.5)
ax.set_ylim(0,0.14)
ax2.set_xlim(7.0,8.0)
def func(x, pos):  # formatter function takes tick label and tick position
    s = str(x)
    ind = s.index('.')
    return s[:ind] + ',' + s[ind+1:]   # change dot to comma
x_format = tkr.FuncFormatter(func)
ax.xaxis.set_major_formatter(x_format)
ax2.xaxis.set_major_formatter(x_format)
# hide the spines between ax and ax2
ax.spines['right'].set_visible(False)
ax2.spines['left'].set_visible(False)
# This looks pretty good, and was fairly painless, but you can get that
# cut-out diagonal lines look with just a bit more work. The important
# thing to know here is that in axes coordinates, which are always
# between 0-1, spine endpoints are at these locations (0,0), (0,1),
# (1,0), and (1,1).  Thus, we just need to put the diagonals in the
# appropriate corners of each of our axes, and so long as we use the
# right transform and disable clipping.

d = .015 # how big to make the diagonal lines in axes coordinates
# arguments to pass plot, just so we don't keep repeating them
kwargs = dict(transform=ax.transAxes, color='k', clip_on=False)
ax.plot((1-d/3,1+d/3), (-d,+d), **kwargs)
ax.plot((1-d/3,1+d/3),(1-d,1+d), **kwargs)

kwargs.update(transform=ax2.transAxes)  # switch to the bottom axes
ax2.plot((-d,+d), (1-d,1+d), **kwargs)
ax2.plot((-d,+d), (-d,+d), **kwargs)
ax2.tick_params(labelright=False)
ax.tick_params(labeltop=False)
ax.tick_params(axis='x', which='major', pad=15)
ax2.tick_params(axis='x', which='major', pad=15)
ax2.set_yticks([])
f.text(0.5, -0.04, 'Tamanho lateral do triângulo ($\mu m$)', ha='center', fontsize=22)
f.text(-0.02, 0.5, 'Frequência relativa', va='center', rotation='vertical', fontsize=22)
#ax.set_xlabel('Tamanho lateral do triângulo ($\mu m$)', fontsize=22)
#ax.set_ylabel('Frequência relativa', fontsize=22)
#x_axis = np.arange(0, 29, 0.001)
#ax.plot(x_axis, norm.pdf(x_axis,2.232,1.888), linewidth=3)
f.tight_layout()
plt.show()
#plt.savefig('output.png', dpi=500, bbox_inches='tight')

尝试使用curve_fit：

#amostra 17B (menor intervalo)
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import lognorm
import matplotlib.ticker as tkr
import scipy, pylab
import locale
import matplotlib.gridspec as gridspec
from scipy.stats import lognorm
locale.setlocale(locale.LC_NUMERIC, "de_DE")
plt.rcParams['axes.formatter.use_locale'] = True
from scipy.optimize import *

frequencia_relativa=[0.000, 0.000, 0.038, 0.097, 0.091, 0.118, 0.070, 0.124, 0.097, 0.059, 0.059, 0.048, 0.054, 0.043, 
                     0.032, 0.005, 0.027, 0.016, 0.005, 0.000, 0.005, 0.000, 0.005, 0.000, 0.000, 0.000, 0.000, 0.000, 
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.000, 0.000]
x=[0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 1.10, 1.20, 1.30, 1.40, 
   1.50, 1.60, 1.70, 1.80, 1.90, 2.00, 2.10, 2.20, 2.30, 2.40, 2.50, 2.60, 2.70, 2.80, 
   2.90, 3.00, 3.10, 3.20, 3.30, 3.40, 3.50, 3.60, 3.70, 3.80, 3.90, 4.00, 4.10, 4.20,
   4.30, 4.40, 4.50, 4.60, 4.70, 4.80, 4.90, 5.00, 5.10, 5.20, 5.30, 5.40, 5.50, 5.60,
   5.70, 5.80, 5.90, 6.00, 6.10, 6.20, 6.30, 6.40, 6.50, 6.60, 6.70, 6.80, 6.90, 7.00,
   7.10, 7.20, 7.30, 7.40, 7.50, 7.60, 7.70, 7.80, 7.90, 8.00]
plt.rcParams["figure.figsize"] = [20,8]
f, (ax,ax2) = plt.subplots(1,2, sharex=True, sharey=True, facecolor='w')
axes = f.add_subplot(111, frameon=False)
ax.spines['top'].set_color('none')
ax2.spines['top'].set_color('none')
gs = gridspec.GridSpec(1,2,width_ratios=[3,1])
ax = plt.subplot(gs[0])
ax2 = plt.subplot(gs[1])
def f(x, mu, sigma) :
   return 1/(np.sqrt(2*np.pi)*sigma*x)*np.exp(-((np.log(x)- 
   mu)**2)/(2*sigma**2))
params, extras = curve_fit(f, x, frequencia_relativa)
plt.plot(x, f(x ,params[0], params[1]))
print("mu=%g, sigma=%g" % (params[0], params[1]))

plt.subplots_adjust(wspace=0.04)
# hide the spines between ax and ax2
ax.spines['right'].set_visible(False)
ax2.spines['left'].set_visible(False)

d = .015 # how big to make the diagonal lines in axes coordinates
# arguments to pass plot, just so we don't keep repeating them
kwargs = dict(transform=ax.transAxes, color='k', clip_on=False)
ax.plot((1-d/3,1+d/3), (-d,+d), **kwargs)
ax.plot((1-d/3,1+d/3),(1-d,1+d), **kwargs)

kwargs.update(transform=ax2.transAxes)  # switch to the bottom axes
ax2.plot((-d,+d), (1-d,1+d), **kwargs)
ax2.plot((-d,+d), (-d,+d), **kwargs)
f.tight_layout()
plt.show()
#plt.savefig('output.png', dpi=500, bbox_inches='tight')

错误：

import matplotlib.ticker as tkr
import scipy, pylab
import locale
import matplotlib.gridspec as gridspec
#from scipy.stats import lognorm
locale.setlocale(locale.LC_NUMERIC, "de_DE")
plt.rcParams['axes.formatter.use_locale'] = True

from scipy.optimize import curve_fit

x=np.asarray([0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 1.10, 1.20, 1.30, 1.40,
   1.50, 1.60, 1.70, 1.80, 1.90, 2.00, 2.10, 2.20, 2.30, 2.40, 2.50, 2.60, 2.70, 2.80,
   2.90, 3.00, 3.10, 3.20, 3.30, 3.40, 3.50, 3.60, 3.70, 3.80, 3.90, 4.00, 4.10, 4.20,
   4.30, 4.40, 4.50, 4.60, 4.70, 4.80, 4.90, 5.00, 5.10, 5.20, 5.30, 5.40, 5.50, 5.60,
   5.70, 5.80, 5.90, 6.00, 6.10, 6.20, 6.30, 6.40, 6.50, 6.60, 6.70, 6.80, 6.90, 7.00,
   7.10, 7.20, 7.30, 7.40, 7.50, 7.60, 7.70, 7.80, 7.90, 8.00], dtype=np.float64)

frequencia_relativa=np.asarray([0.000, 0.000, 0.038, 0.097, 0.091, 0.118, 0.070, 0.124, 0.097, 0.059, 0.059, 0.048, 0.054, 0.043,
                     0.032, 0.005, 0.027, 0.016, 0.005, 0.000, 0.005, 0.000, 0.005, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.000, 0.000], dtype=np.float64)

f, (ax,ax2) = plt.subplots(1,2, sharex=True, sharey=True, facecolor='w')

def fun(y, mu, sigma):
    return 1.0/(np.sqrt(2.0*np.pi)*sigma*y)*np.exp(-(np.log(y)-mu)**2/(2.0*sigma*sigma))

step = 0.1

xx = x

nrm = np.sum(frequencia_relativa*step) # normalization integral
print(nrm)

frequencia_relativa /= nrm # normalize frequences histogram

print(np.sum(frequencia_relativa*step)) # check normalizatio

params, extras = curve_fit(fun, xx, frequencia_relativa)

print(params[0])
print(params[1])

axes = f.add_subplot(111, frameon=False)

axes.plot(x, fun(x, params[0], params[1]), "b-", linewidth=3)


ax.spines['top'].set_color('none')
ax2.spines['top'].set_color('none')
gs = gridspec.GridSpec(1,2,width_ratios=[3,1])
ax = plt.subplot(gs[0])
ax2 = plt.subplot(gs[1])
ax.axvspan(0.190, 1.616, label='Média $\pm$ desvio padrão', ymin=0.0, ymax=1.0, alpha=0.2, color='Plum')
ax.yaxis.tick_left()
ax.xaxis.tick_bottom()
ax2.xaxis.tick_bottom()
ax.tick_params(labeltop='off') # don't put tick labels at the top
ax2.yaxis.tick_right()
ax.bar(xx, height=frequencia_relativa, label='Frequência relativa do tamanho lateral triangular', alpha=0.5, width=0.1, align='edge', edgecolor='black', hatch="///")
ax2.bar(xx, height=frequencia_relativa, alpha=0.5, width=0.1, align='edge', edgecolor='black', hatch="///")
#plt.plot(xx, frequencia_relativa, "ro")
ax.tick_params(axis = 'both', which = 'major', labelsize = 18)
ax.tick_params(axis = 'both', which = 'minor', labelsize = 18)
ax2.tick_params(axis = 'both', which = 'major', labelsize = 18)
ax2.tick_params(axis = 'both', which = 'minor', labelsize = 18)
ax2.xaxis.set_ticks(np.arange(7.0, 8.5, 0.5))
ax2.xaxis.set_major_formatter(tkr.FormatStrFormatter('%0.1f'))

plt.subplots_adjust(wspace=0.04)
ax.set_xlim(0,2.5)
ax.set_ylim(0,1.4)
ax2.set_xlim(7.0,8.0)
def func(x, pos):  # formatter function takes tick label and tick position
    s = str(x)
    ind = s.index('.')
    return s[:ind] + ',' + s[ind+1:]   # change dot to comma
x_format = tkr.FuncFormatter(func)
ax.xaxis.set_major_formatter(x_format)
ax2.xaxis.set_major_formatter(x_format)
# hide the spines between ax and ax2
ax.spines['right'].set_visible(False)
ax2.spines['left'].set_visible(False)

d = .015 # how big to make the diagonal lines in axes coordinates
# arguments to pass plot, just so we don't keep repeating them
kwargs = dict(transform=ax.transAxes, color='k', clip_on=False)
ax.plot((1-d/3,1+d/3), (-d,+d), **kwargs)
ax.plot((1-d/3,1+d/3),(1-d,1+d), **kwargs)

kwargs.update(transform=ax2.transAxes)  # switch to the bottom axes
ax2.plot((-d,+d), (1-d,1+d), **kwargs)
ax2.plot((-d,+d), (-d,+d), **kwargs)
ax2.tick_params(labelright=False)
ax.tick_params(labeltop=False)
ax.tick_params(axis='x', which='major', pad=15)
ax2.tick_params(axis='x', which='major', pad=15)
ax2.set_yticks([])
f.text(0.5, -0.04, 'Tamanho lateral do triângulo ($\mu m$)', ha='center', fontsize=22)
f.text(-0.02, 0.5, 'Frequência relativa', va='center', rotation='vertical', fontsize=22)
#ax.set_xlabel('Tamanho lateral do triângulo ($\mu m$)', fontsize=22)
#ax.set_ylabel('Frequência relativa', fontsize=22)
#x_axis = np.arange(0, 29, 0.001)
#ax.plot(x_axis, norm.pdf(x_axis,2.232,1.888), linewidth=3)

ax.axvline(0.903, color='k', linestyle='-', linewidth=1.3)
ax.axvline(0.190, color='k', linestyle='--', linewidth=1)
ax.axvline(1.616, color='k', linestyle='--', linewidth=1)
f.legend(loc=9, 
          bbox_to_anchor=(.79,.99),
          labelspacing=1.5,
          numpoints=1,
          columnspacing=0.2,
          ncol=1, fontsize=18)
ax.text(0.903*0.70, 1.4*0.92, '$\mu$ = (0,90 $\pm$ 0,71) $\mu m$', fontsize=20)
f.tight_layout()

plt.show()

塞弗林·帕帕德（Severin Pappadeux）

您正在尝试同时制作花式图和拟合图。您可以帮助您适应健康，图形是第二个问题。

首先，使用NumPy数组存储数据，会有所帮助。其次，您的直方图函数被归一化。

因此，如果在您的第一个程序中，我将规范freqs数组

x=np.asarray([0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 1.10, 1.20, 1.30, 1.40,
   1.50, 1.60, 1.70, 1.80, 1.90, 2.00, 2.10, 2.20, 2.30, 2.40, 2.50, 2.60, 2.70, 2.80,
   2.90, 3.00, 3.10, 3.20, 3.30, 3.40, 3.50, 3.60, 3.70, 3.80, 3.90, 4.00, 4.10, 4.20,
   4.30, 4.40, 4.50, 4.60, 4.70, 4.80, 4.90, 5.00, 5.10, 5.20, 5.30, 5.40, 5.50, 5.60,
   5.70, 5.80, 5.90, 6.00, 6.10, 6.20, 6.30, 6.40, 6.50, 6.60, 6.70, 6.80, 6.90, 7.00,
   7.10, 7.20, 7.30, 7.40, 7.50, 7.60, 7.70, 7.80, 7.90, 8.00], dtype=np.float64)

frequencia_relativa=np.asarray([0.000, 0.000, 0.038, 0.097, 0.091, 0.118, 0.070, 0.124, 0.097, 0.059, 0.059, 0.048, 0.054, 0.043,
                     0.032, 0.005, 0.027, 0.016, 0.005, 0.000, 0.005, 0.000, 0.005, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.000, 0.000], dtype=np.float64)

step = 0.1

nrm = np.sum(frequencia_relativa*step) # normalization integral
print(nrm)

frequencia_relativa /= nrm

print(np.sum(frequencia_relativa*step))

并将Y限制设置为1.4，我将获得以下图表

然后，在拟合部分中，我将进行类似的转换，并将X轴移动一半步长，以便直方图值位于bin的中间，fit开始起作用，代码，Python 3.9.1 Win 10 x64 。我删除了与拟合无关的所有内容，以便对您有用，并绘制了拟合函数与输入数据的关系。

我也不太了解对积分进行归一化的部分（直方图中所有条形的总和为1，因为它是相对频率），我也不了解步进和移位的选择。您能更好地解释这一部分吗？

您要拟合的函数是对数范数分布的两个参数PDF。它条件，使得₀＆Integral; ^∞ PDF（X，μ，σ）= 1。您必须以相同的方式处理输入数据。对于直方图，积分是箱的总和乘以步长。步长显然为0.1，因此我计算了该总和，检查它是否为1，然后将频率除以归一化值，以使积分等于1。您可以尝试拟合非2参数曲线，而不是3参数曲线，第三参数是归一化值，但是非线性拟合中的更多参数意味着您可能会遇到更多问题。

Wrt移位，必须做出一个假设，即bin的值描述了什么。我假设bin的值应该是bin中间的值。再次，这是一个假设，我不知道您的数据是如何生成的，也许直方图的值实际上是bin左侧的值。就是这样，您只需要删除移位并重新运行代码即可。

import numpy as np
import matplotlib.pyplot as plt

from scipy.optimize import curve_fit

x=np.asarray([0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 1.10, 1.20, 1.30, 1.40,
   1.50, 1.60, 1.70, 1.80, 1.90, 2.00, 2.10, 2.20, 2.30, 2.40, 2.50, 2.60, 2.70, 2.80,
   2.90, 3.00, 3.10, 3.20, 3.30, 3.40, 3.50, 3.60, 3.70, 3.80, 3.90, 4.00, 4.10, 4.20,
   4.30, 4.40, 4.50, 4.60, 4.70, 4.80, 4.90, 5.00, 5.10, 5.20, 5.30, 5.40, 5.50, 5.60,
   5.70, 5.80, 5.90, 6.00, 6.10, 6.20, 6.30, 6.40, 6.50, 6.60, 6.70, 6.80, 6.90, 7.00,
   7.10, 7.20, 7.30, 7.40, 7.50, 7.60, 7.70, 7.80, 7.90, 8.00], dtype=np.float64)

frequencia_relativa=np.asarray([0.000, 0.000, 0.038, 0.097, 0.091, 0.118, 0.070, 0.124, 0.097, 0.059, 0.059, 0.048, 0.054, 0.043,
                     0.032, 0.005, 0.027, 0.016, 0.005, 0.000, 0.005, 0.000, 0.005, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.000, 0.000], dtype=np.float64)

def f(y, mu, sigma):
    return 1/(np.sqrt(2.0*np.pi)*sigma*y)*np.exp(-(np.log(y)-mu)**2/(2.0*sigma*sigma))

step = 0.1

nrm = np.sum(frequencia_relativa*step)

frequencia_relativa /= nrm

xx = x - 0.5*step

params, extras = curve_fit(f, xx, frequencia_relativa)

mu = params[0]
sigma = params[1]

print((mu,sigma))

# calculate mean value, https://en.wikipedia.org/wiki/Log-normal_distribution
print(np.exp(mu + sigma*sigma/2.0))

# calculate stddev as sq.root of variance
z=np.sqrt((np.exp(sigma*sigma)-1)*np.exp(mu+mu+sigma*sigma))
print(z)

xxx=np.linspace(0.001,8,1000)
plt.plot(xxx, f(xxx, mu, sigma), "b-")
plt.plot(xx, frequencia_relativa, "ro")

plt.show()

而且我得到的lognorm曲线看起来像输入数据一样好。两条曲线在[0 ... 2]区间中都有大部分数据，峰值约为〜（0.8，1.2）。这是最简单的图，它使拟合曲线（蓝色）与频率直方图块（红色点）的中心重叠。现在，您可以尝试将其放入精美的图表中，祝您好运。

仅作参考，适合3参数对数-范数曲线的代码适用于非规格化数据。似乎也能正常工作

import numpy as np
import matplotlib.pyplot as plt

from scipy.optimize import curve_fit

x=np.asarray([0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 1.10, 1.20, 1.30, 1.40,
   1.50, 1.60, 1.70, 1.80, 1.90, 2.00, 2.10, 2.20, 2.30, 2.40, 2.50, 2.60, 2.70, 2.80,
   2.90, 3.00, 3.10, 3.20, 3.30, 3.40, 3.50, 3.60, 3.70, 3.80, 3.90, 4.00, 4.10, 4.20,
   4.30, 4.40, 4.50, 4.60, 4.70, 4.80, 4.90, 5.00, 5.10, 5.20, 5.30, 5.40, 5.50, 5.60,
   5.70, 5.80, 5.90, 6.00, 6.10, 6.20, 6.30, 6.40, 6.50, 6.60, 6.70, 6.80, 6.90, 7.00,
   7.10, 7.20, 7.30, 7.40, 7.50, 7.60, 7.70, 7.80, 7.90, 8.00], dtype=np.float64)

frequencia_relativa=np.asarray([0.000, 0.000, 0.038, 0.097, 0.091, 0.118, 0.070, 0.124, 0.097, 0.059, 0.059, 0.048, 0.054, 0.043,
                     0.032, 0.005, 0.027, 0.016, 0.005, 0.000, 0.005, 0.000, 0.005, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
                     0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.005, 0.000, 0.000], dtype=np.float64)

def f(y, mu, sigma, N):
    return N/(np.sqrt(2.0*np.pi)*sigma*y)*np.exp(-(np.log(y)-mu)**2/(2.0*sigma*sigma))

step = 0.1

xx = x - 0.5*step

params, extras = curve_fit(f, xx, frequencia_relativa)

print(params)

plt.plot(xx, f(xx, params[0], params[1], params[2]), "b-")
plt.plot(xx, frequencia_relativa, "ro")

plt.show()

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编辑于2021-02-24

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