如何在scipy.stats.gamma.fit中获取适合参数的误差估计? [英] How to get error estimates for fit parameters in scipy.stats.gamma.fit?

问题描述

我有一些适合使用scipy.stats的伽马分布.我能够提取形状，位置和比例参数，并且它们与我期望的数据范围看起来很合理.

I have some which I am fitting to the gamma distribution using scipy.stats. I am able to extract the shape, loc, and scale params and they look reasonable with the data ranges I expect.

我的问题是:是否有一种方法也可以获取参数中的错误?类似于curve_fit的输出.注意:我不直接使用曲线拟合，因为它无法正常工作，并且大多数时候无法计算伽玛分布的参数.另一方面，scipy.stats.gamma.fit可以正常工作.

My question is: is there a way to also get the errors in the parameters? something like the output of curve_fit. NOTE: I don't use curve fit directly because it is not working properly and most of the time is not able to compute the parameters of the gamma distribution. On the other hand, scipy.stats.gamma.fit works ok.

这是我正在做的事的一个例子(没有我的实际数据).

This is an example (no my actual data) of what I am doing.

from scipy.stats import gamma
shape = 12; loc = 0.71; scale = 0.0166
data = gamma.rvs(shape, loc=loc, scale=scale, size=1000)
params = gamma.fit(data) # params close to but not the same as (shape, loc, scale) 
# HOW TO ESTIMATE/GET ERRORS FOR EACH PARAM?

预先感谢

推荐答案

编辑警告:以下问题示例说明了 GenericLikelihoodModel 的用法.但是，在伽马分布的情况下，位置参数会改变对分布的支持，而对于最大似然估计的一般假设则排除了这种支持.更标准的用法将固定支持，floc = 0，因此它只是一个两参数分布.在这种情况下，适用标准的MLE理论.

edit Warning: The following illustrates the use of GenericLikelihoodModel following the example in the question. However, in the case of the gamma distribution the location parameter shifts the support of the distribution which is ruled out by the general assumptions for maximum likelihood estimation. The more standard usage would fix the support, floc=0, so it is just a two-parameter distribution. In that case, standard MLE theory applies.

Statsmodels具有用于最大似然估计的通用类 GenericLikelihoodModel .它不是直接为这种情况设计的，但可以在一些帮助下使用(定义属性并提供start_params).

Statsmodels has a generic class for maximum likelihood estimation, GenericLikelihoodModel. It's not directly designed for this case, but can be used with some help (defining attributes and providing start_params).

import numpy as np
from statsmodels.base.model import GenericLikelihoodModel

from scipy.stats import gamma
shape = 12; loc = 0.71; scale = 0.0166
data = gamma.rvs(shape, loc=loc, scale=scale, size=1000)
params = gamma.fit(data) # params close to but not the same as (shape, loc, scale) 
# HOW TO ESTIMATE/GET ERRORS FOR EACH PARAM?

print(params)
print('\n')


class Gamma(GenericLikelihoodModel):

    nparams = 3

    def loglike(self, params):
        return gamma.logpdf(self.endog, *params).sum()


res = Gamma(data).fit(start_params=params)
res.df_model = len(params)
res.df_resid = len(data) - len(params)
print(res.summary())

这将打印以下内容

(10.31888758604304, 0.71645502437403186, 0.018447479022445423)


Optimization terminated successfully.
         Current function value: -1.439996
         Iterations: 69
         Function evaluations: 119
                                Gamma Results                                 
==============================================================================
Dep. Variable:                      y   Log-Likelihood:                 1440.0
Model:                          Gamma   AIC:                            -2872.
Method:            Maximum Likelihood   BIC:                            -2852.
Date:                Sun, 12 Jul 2015                                         
Time:                        04:00:05                                         
No. Observations:                1000                                         
Df Residuals:                     997                                         
Df Model:                           3                                         
==============================================================================
                 coef    std err          z      P>|z|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
par0          10.3187      2.242      4.603      0.000         5.925    14.712
par1           0.7165      0.019     37.957      0.000         0.679     0.753
par2           0.0184      0.002      8.183      0.000         0.014     0.023
==============================================================================

然后也可以使用基于最大似然估计的其他结果，例如可以通过指定限制矩阵或使用具有等式的字符串表达式来执行第一个参数为10的z检验.

Other results based on the maximum likelihood estimates are then also available, for example a z-test that the first parameter is 10 can be performed like either by specifying a restriction matrix or by using a string expression with the equality:

>>> res.t_test(([1, 0, 0], [10]))
<class 'statsmodels.stats.contrast.ContrastResults'>
                             Test for Constraints                             
==============================================================================
                 coef    std err          z      P>|z|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
c0            10.3187      2.242      0.142      0.887         5.925    14.712
==============================================================================

>>> res.t_test('par0=10')
<class 'statsmodels.stats.contrast.ContrastResults'>
                             Test for Constraints                             
==============================================================================
                 coef    std err          z      P>|z|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
c0            10.3187      2.242      0.142      0.887         5.925    14.712
==============================================================================

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