为什么 Johnson-SU 分布在 scipy.stats 中不给出正偏度?

下面的代码映射了对应参数(a、b、loc)生成的统计矩(均值、方差、偏度、超峰度)>, scale) Johnson-SU 分布 (johnsonsu).

The code below maps the statistical moments (mean, variance, skewness, excess kurtosis) generated by corresponding parameters (a, b, loc, scale) of the Johnson-SU distribution (johnsonsu).

对于我在下面的代码中指定的循环值范围，没有参数配置会导致正偏度，只有负偏度，即使应该可以将 Johnson-SU 分布参数化为正偏度.

For the range of loop values specified in my code below, no parameter configuration results in positive skewness, only negative skewness, even though it should be possible to parameterize the Johnson-SU distribution to be positively-skewed.

import numpy as np
import pandas as pd
from scipy.stats import johnsonsu

moments = ['mu','sd','sk','ku']
X = []
for a in np.arange(0.5,5,.5):
    for b in np.arange(0.5,5,.5):
        for c in np.arange(-0.5,0.5,.25): #loc
            for d in [1]: #scale
                mvsk = johnsonsu.stats(a,b,c,d,moments='mvsk')
                mvsk = [mvsk[i].tolist() for i in range(len(mvsk))]
                X.append([a,b,c,d]+mvsk)
X = pd.DataFrame(np.asarray(X), columns=['a','b','c','d']+moments)   

for m in moments:
    print(m, X[[m]].min().round(3).values[0], X[[m]].max().round(3).values[0])

打印的最小和最大时刻是:

The min and max moments printed are:

mu -29937.57 0.136
sd 0.053 48036174150.987
sk -414.36 -0.078
ku 0.221 41173.869

探索 a、b、loc 和 scale 参数的范围比什么更好我在下面指定了?文档只说a 和 b 必须是正数，没有关于 loc 和 scale 必须限制的内容.

What would be better ranges to explore for the a, b, loc and scale parameters than what I have specified below? The documentation only says a and b must be positive, nothing about what loc and scale must be limited to.