Issuse: Scipy 拟合正态数据

Question

我目前导入并绘制了一些正态分布的实验数据。

然后我尝试使用 Scipy 来适应数据的正常分布：

from scipy.stats import norm

def normal_fit(data, offset):
    x = numpy.linspace(0, len(data), len(data))
    params = norm.fit(data - offset)
    normal = norm.pdf(x, params[0], params[1])

    return normal, params

但是它计算出的均值和标准差 (4504, 2961) 是不正确的 - 在下面以红色绘制。

如何正确拟合数据？

编辑： 按照 ev-br 的建议，数据偏移为零，这会产生仍然没有多大意义的参数 (954, 2961)

Answer 1

需要先减去零级

Answer 2

我玩过类似的问题

添加了b，曲线拟合的偏移量，似乎需要一个半途OK的猜测值

然后比例因子符号变了？？ to 我刚补过，不懂自己

这里是使用 curve_fit 重新编写的代码，还找到了偏移量：

from scipy.stats import norm
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

x = np.array([ 0.47712125,  0.5445641 ,  0.61193563,  0.67924615,  0.74671202,
    0.81404772,  0.88144172,  0.94885291,  1.01623919,  1.08361011,
    1.15100191,  1.21837793,  1.28578227,  1.3531658 ,  1.42054981,
    1.48794397,  1.55532424,  1.62272161,  1.69010744,  1.75749472,
    1.82488047,  1.89226717,  1.9596566 ,  2.02704774,  2.09443269,
    2.16182302,  2.2292107 ,  2.29659719,  2.36398595,  2.43137342,
    2.49876254,  2.56614983,  2.63353814,  2.700926  ,  2.76831392,
    2.83570198,  2.90308999,  2.97008999,  3.03708997,  3.10408999,
    3.17108999,  3.23808998,  3.30508998,  3.37208999,  3.43908999,
    3.50608998,  3.57308998,  3.64008999,  3.70708999,  3.77408999,
    3.84108999,  3.90808999])/2
y = np.array([  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
     0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
     0.00000000e+00,   5.50000000e+01,   1.33500000e+02,
     2.49000000e+02,   4.40000000e+02,   7.27000000e+02,
     1.09000000e+03,   1.53000000e+03,   2.21500000e+03,
     3.13500000e+03,   4.44000000e+03,   5.57000000e+03,
     6.77000000e+03,   8.04500000e+03,   9.15500000e+03,
     1.00000000e+04,   1.06000000e+04,   1.06500000e+04,
     1.02000000e+04,   9.29000000e+03,   8.01500000e+03,
     6.50000000e+03,   5.24000000e+03,   4.11000000e+03,
     2.97000000e+03,   1.86000000e+03,   1.02000000e+03,
     5.26500000e+02,   2.49000000e+02,   1.11000000e+02,
     5.27000000e+01,   6.90825000e+00,   4.54329000e+00,
     3.63846500e+00,   3.58135000e+00,   2.37404000e+00,
     1.81840000e+00,   1.20159500e+00,   6.02470000e-01,
     3.43295000e-01,   1.62295000e-01,   7.99350000e-02,
     3.60750000e-02,   1.50000000e-02,   3.61500000e-03,
     8.00000000e-05])+10000
#numpy.random.normal(loc=0.0, scale=2.0, size=100)
'''
norm.pdf(x) = exp(-x**2/2)/sqrt(2*pi)
norm.pdf(x, loc, scale) == norm.pdf(y) / scale with y = (x - loc) / scale
'''
def datafit(x,N,u,sig,b):
    y = N*np.exp(-((x-u)/sig)**2/2)/(np.sqrt(2*np.pi)) + b
    return y
popt,popc = curve_fit(datafit,x,y,p0=[np.max(y),2,2,1000])

# scipy norm.pdf with scaling factors to match datafit()
scale = abs(popt[2]) # I don't know why, but it 1s needed with b
Normal_distribution = popt[0]*scale*norm.pdf(x, popt[1], scale) + popt[3]


plt.plot(x,y, 'b-')
plt.plot(x, datafit(x+.1, *popt), 'g')
plt.plot(x, Normal_distribution, 'r')

Issuse: Scipy 拟合正态数据

Issuse: Scipy Fitting Normal Data

python

numpy

scipy

data-fitting