使用scipy.optimize非常适合对数正态密度函数

Question

我正在尝试使用以下密度函数校准对数正态分布的参数mu和sigma：

xdata:
4.870000000000000760e-09
5.620000000000000859e-09
6.490000000000000543e-09
7.500000000000000984e-09
8.660000000000001114e-09
1.000000000000000021e-08
1.155000000000000085e-08
1.334000000000000067e-08
1.540000000000000224e-08
1.778000000000000105e-08
2.054000000000000062e-08
2.371000000000000188e-08
2.738000000000000099e-08
3.162000000000000124e-08
3.652000000000000541e-08
4.217000000000000637e-08
4.870000000000000595e-08
5.623000000000000125e-08
6.493999999999999784e-08
7.498999999999999850e-08
8.659999999999999460e-08
1.000000000000000087e-07
1.154800000000000123e-07
1.333500000000000129e-07
1.539900000000000177e-07
1.778300000000000247e-07
2.053499999999999958e-07
2.371399999999999913e-07
2.738399999999999692e-07
3.162300000000000199e-07
3.651700000000000333e-07
4.217000000000000240e-07
4.869700000000000784e-07
8.659600000000001124e-07
1.000000000000000167e-06


ydata:
1.883186407957446899e+11
3.609524622222222290e+11
7.508596384507042236e+11
2.226776878843930664e+12
4.845941940346821289e+12
7.979258430057803711e+12
1.101088735028901758e+13
1.346205871213872852e+13
1.509035024739884375e+13
1.599175638381502930e+13
1.668097844161849805e+13
1.786208191445086719e+13
2.007139089017341016e+13
2.346096336416185156e+13
2.763042850867051953e+13
3.177726578034682031e+13
3.552045143352600781e+13
3.858765218497110156e+13
4.051697248554913281e+13
4.132681209248554688e+13
4.112713068208092188e+13
4.003871248554913281e+13
3.797625966473988281e+13
3.472541513294797656e+13
3.017757826589595312e+13
2.454670317919075000e+13
1.840085110982658984e+13
1.250047161156069336e+13
7.540309609248554688e+12
3.912091102658959473e+12
1.632974141040462402e+12
4.585002890867052002e+11
1.260128910303030243e+11
7.276263267445255280e+09
1.120399584203921509e+10

绘制时，密度函数如下所示：

如果我现在尝试通过执行以下操作来获得两个参数mu和sigma的最佳匹配：

def func(x, mu, sigma):
    return 1 / x * 1 / (sigma * np.sqrt(2*np.pi)) * np.exp(-(np.log(x)-mu)**2/(2*sigma**2))

popt, pcov = curve_fit(func, xdata, ydata)

plt.plot(xdata, func(xdata, *popt), label='fitted')

结果图如下：

不仅比例完全不同，而且与原始的密度函数甚至都远非如此。

如何使用Python获得适合我的密度函数？