使用最大似然估计器实现的曲线拟合不起作用

Question

我正在为离散计数数据实现最大似然估计，以便进行曲线拟合，实现一个curve_fit函数，用作scipy中最小化函数的初始猜测参数。我为多个发行版定义并尝试了这些方法，但为简单起见只包含一个，这是一个logseries发行版。

此时我还尝试了statsmodels方法的以下方法：1。statsmodels.discrete.discrete_model.fit 2. statsmodels.discrete.count_model.fit 3. statsmodels.base.model.GenericLikelihoodModel

大多数曲线拟合往往会遇到溢出错误或内部的零和零。我将在另一篇文章中详细说明这些错误

#Import a few packages
import numpy as np
from scipy.optimize import curve_fit
from scipy.optimize import minimize
from scipy import stats
from numpy import log
import numpy as np
import matplotlib.pyplot as plt

#Given data
x=np.arange(1, 28, 1)
y=np.array([18899, 10427, 6280, 4281, 2736, 1835, 1158, 746, 467, 328, 201, 129, 65, 69, 39, 21, 15, 10, 3, 3, 1, 1, 1, 1, 1, 1, 1])

#Define a custom distribution
def Logser(x, p): 
    return (-p**x)/(x*log(1-p))

#Doing a least squares curve fit
def lsqfit(x, y):
 cf_result = curve_fit(Logser, x, y, p0=0.7, bounds=(0.5,1), method='trf') 
 return cf_result

param_guess=lsqfit(x,y)[0][0]   
print(param_guess)

#Doing a custom MLE definition, minimized using the scipy minimize function

def MLERegression(param_guess):  
 yhat = Logser(x, param_guess) # predictions based on a parameter value
 sd=1 #initially guessed for fitting a normal distribution error around the regressed curve
# next, we flip the Bayesian question
# compute PDF of observed values normally distributed around mean (yhat)
# with a standard deviation of sd
 negLL = -np.sum( stats.norm.logpdf(y, loc=yhat, scale=sd) ) #log of the probability density function
 return negLL

results = minimize(MLERegression, param_guess, method='L-BFGS-B', bounds=(0.5,1.0), options={'disp': True})
final_param=results['x']
print(final_param)

我已经限制优化器给我类似于我期望的结果（参数值大约为0.8或0.9）。否则算法输出零

Answer 1

我认为这是由于扩展。当我通过添加比例因子将等式更改为“scale *（ - p ** X）/（X * log（1-p））”时，我得到以下值而不使用任何边界：p = 9.0360470735534726E-01和scale = 5.1189277041342692E + 04产生以下结果：

而我对p的拟合值确实是0.9。