拟合自定义Scipy分布 [英] Fitting a Custom Scipy Distribution
问题描述
我已经使用自定义scipy类重新定义了对数正态分布.我已经模拟了这种分布,并且尝试恢复指定的原始参数,但是fit方法返回不同的参数.
I have redefined the lognormal distribution using custom scipy class. I have simulated this distribution and I am trying to recover the original parameters I have specified, however, the fit method is returning different parameters.
import numpy as np
import pandas as pd
from scipy.stats import rv_continuous
from scipy.special import erf
from scipy.special import erfinv
class lognorm_v2(rv_continuous):
def _pdf(self, x, mu, sigma):
return 1 / (x * sigma * np.sqrt(2 * np.pi)) * np.exp(-0.5 * ((np.log(x) - mu)/sigma)**2)
def _cdf(self, x, mu, sigma):
return 0.5 + 0.5 * erf((np.log(x) - mu)/ (np.sqrt(2)*sigma))
def _sf(self, x, mu, sigma):
u = (x)**b/(1+x**b)
return 1 - 0.5 + 0.5 * erf((np.log(x) - mu)/ (np.sqrt(2)*sigma))
def _ppf(self,x, mu, sigma):
return np.exp(sigma * erfinv(2*x - 1) - mu)
def _argcheck(self, mu, sigma):
s = sigma > 0
return s
np.random.seed(seed=111)
logn = lognorm_v2(name='lognorm_v2',a=0,b=np.inf)
test = logn.rvs(mu=2,sigma=1,loc=0,scale=1,size=100000)
logn.fit(test)
logn.fit(test,floc=0,fscale=1)
当位置和比例不固定时,我获取参数:
When loc and scale are not fixed I obtain the parameters:
(0.9216388162274325,0.7061876689651909,-0.0003659266464081178,0.05399544825451739)
(0.9216388162274325, 0.7061876689651909, -0.0003659266464081178, 0.05399544825451739)
固定后,结果为:
(-2.0007136838780917,0.7086144279779958,0,1)
(-2.0007136838780917, 0.7086144279779958, 0, 1)
为什么我不能提取原始模拟中指定的mu 2和sigma 1?我知道我将无法获得确切的值,但是对于100K模拟来说,它们应该非常接近.我的numpy版本是1.19.2,scipy是1.5.2.谢谢!
Why am I not able to extract the mu 2 and sigma 1 specified in the original simulation? I understand I will not get the exact values, but they should be very close for 100K simulations. My numpy is version 1.19.2 and scipy is 1.5.2. Thank you!
推荐答案
我已使用正确的_ppf更正了代码,似乎可以为mu和sigma产生适当的匹配度
I've corrected code with proper _ppf, and it seems to produce proper fits for mu and sigma
代码,Python 3.9 Windows 10 x64
Code, Python 3.9 Windows 10 x64
import numpy as np
from scipy.stats import rv_continuous
from scipy.special import erf
from scipy.special import erfinv
SQRT2 = np.float64(1.4142135623730951)
class lognorm_v2(rv_continuous):
def _pdf(self, x, μ, σ):
return 1 / (x * σ * SQRT2 * np.sqrt(np.pi)) * np.exp(-0.5 * ((np.log(x) - μ)/σ)**2)
def _cdf(self, x, μ, σ):
return 0.5 + 0.5 * erf((np.log(x) - μ)/ (SQRT2*σ))
def _ppf(self, x, μ, σ):
return np.exp(μ + σ * SQRT2 * erfinv(2.0*x - 1.0))
def _argcheck(self, μ, σ):
s = σ > 0.0
return s
np.random.seed(seed=111)
logn = lognorm_v2(name='lognorm_v2', a=0.0, b=np.inf)
test = logn.rvs(μ=2.0,σ=1.0,loc=0.0,scale=1.0, size=100000)
logn.fit(test,floc=0,fscale=1)
打印出
(1.9990788106319746, 1.0021523463000124, 0, 1)
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