问题描述
我想使用 python scipy.stats.lognormal.fit 将对数正态分布拟合到我的数据中.根据手册，fit 返回 shape, loc, scale 参数.但是，对数正态分布通常只需要两个参数:均值和标准差.
I want to fit lognormal distribution to my data, using python scipy.stats.lognormal.fit. According to the manual, fit returns shape, loc, scale parameters. But, lognormal distribution normally needs only two parameters: mean and standard deviation.
如何解释 scipy fit 函数的结果?如何获得均值和标准差.
How to interpret the results from scipy fit function? How to get mean and std.dev.?
推荐答案
scipy 中的分布以通用方式编码，包含两个参数 location 和 scale，因此 location 是参数 (loc)将分布向左或向右移动，而 scale 是压缩或拉伸分布的参数.
The distributions in scipy are coded in a generic way wrt two parameter location and scale so that location is the parameter (loc) which shifts the distribution to the left or right, while scale is the parameter which compresses or stretches the distribution.
对于两个参数对数正态分布，mean"和std dev"分别对应log(scale)和shape(可以让loc=0).
For the two parameter lognormal distribution, the "mean" and "std dev" correspond to log(scale) and shape (you can let loc=0).
以下说明如何拟合对数正态分布以找到两个感兴趣的参数:
The following illustrates how to fit a lognormal distribution to find the two parameters of interest:
In [56]: import numpy as np
In [57]: from scipy import stats
In [58]: logsample = stats.norm.rvs(loc=10, scale=3, size=1000) # logsample ~ N(mu=10, sigma=3)
In [59]: sample = np.exp(logsample) # sample ~ lognormal(10, 3)
In [60]: shape, loc, scale = stats.lognorm.fit(sample, floc=0) # hold location to 0 while fitting
In [61]: shape, loc, scale
Out[61]: (2.9212650122639419, 0, 21318.029350592606)
In [62]: np.log(scale), shape # mu, sigma
Out[62]: (9.9673084420467362, 2.9212650122639419)
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