Fitting Lognormal Data

[Carolyn]

Thank you for your answer!

I think i have to ask my question more precise.

I have 2 arrays, one of x-data, one of y-data:

x-data array:

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array([[19.8815 ],
[19.0141 ],
[18.1857 ],
[17.3943 ],
[16.6382 ],
[15.9158 ],
[15.2254 ],
[14.5657 ],
[13.9352 ],
[13.3325 ],
[12.7564 ],
[12.2056 ],
[11.679 ],
[11.1755 ],
[10.6941 ],
[10.2338 ],
[ 9.79353],
[ 9.37249],
[ 8.96979],
[ 8.58462],
[ 8.21619],
[ 7.86376],
[ 7.52662],
[ 7.20409],
[ 6.89552],
[ 6.6003 ],
[ 6.31784],
[ 6.04757],
[ 5.78897],
[ 5.54151],
[ 5.30472],
[ 5.07812],
[ 4.86127],
[ 4.65375],
[ 4.45514],
[ 4.26506],
[ 4.08314],
[ 3.90903],
[ 3.74238],
[ 3.58288],
[ 3.4302 ],
[ 3.28407],
[ 3.14419],
[ 3.01029],
[ 2.88212],
[ 2.75943],
[ 2.64198],
[ 2.52955],
[ 2.42192],
[ 2.31889],
[ 2.22026],
[ 2.12583],
[ 2.03543],
[ 1.94889],
[ 1.86604],
[ 1.78671],
[ 1.71077],
[ 1.63807],
[ 1.56845],
[ 1.50181],
[ 1.43801],
[ 1.37691],
[ 1.31842],
[ 1.26242],
[ 1.2088 ],
[ 1.15746],
[ 1.10832],
[ 1.06126],
[ 1.01619]])

y-data array:

array([[1.01567e+03],
[8.18397e+02],
[7.31992e+02],
[1.11397e+03],
[2.39987e+03],
[2.73762e+03],
[4.65722e+03],
[7.06308e+03],
[9.67945e+03],
[1.38983e+04],
[1.98178e+04],
[1.97461e+04],
[3.28070e+04],
[4.48814e+04],
[5.80853e+04],
[7.35511e+04],
[8.94090e+04],
[1.08274e+05],
[1.28276e+05],
[1.50281e+05],
[1.69258e+05],
[1.91944e+05],
[2.16416e+05],
[2.37259e+05],
[2.57426e+05],
[2.74818e+05],
[2.90343e+05],
[3.01369e+05],
[3.09232e+05],
[3.13713e+05],
[3.17225e+05],
[3.19177e+05],
[3.17471e+05],
[3.14415e+05],
[3.08396e+05],
[2.95692e+05],
[2.76097e+05],
[2.52075e+05],
[2.29330e+05],
[1.97843e+05],
[1.74262e+05],
[1.46360e+05],
[1.20599e+05],
[9.82223e+04],
[7.80995e+04],
[6.34618e+04],
[4.77460e+04],
[3.88737e+04],
[3.23715e+04],
[2.58129e+04],
[2.15724e+04],
[1.58737e+04],
[1.13006e+04],
[7.64983e+03],
[4.64590e+03],
[3.31463e+03],
[2.40929e+03],
[3.02183e+03],
[1.47422e+03],
[1.06046e+03],
[1.34875e+03],
[8.26674e+02],
[9.53167e+02],
[6.47428e+02],
[9.83651e+02],
[8.93673e+02],
[1.23637e+03],
[0.00000e+00],
[8.36573e+01]])

Plotting this, i geht the graph that i postet yesterday. Its clearly a lognormal function, so what i need now is a (lognormal-) function, that fits my data best, to gain the median and the sigma. I thought, that "stats.lognorm.fit" provides me this information. Unfortunately when i run the following code, i get a median of approximately 1.4, but looking at my graph, it clearly should be somewhere around 6.

from scipy import stats
 
 s, loc, scale = stats.lognorm.fit(x0, floc=0) #x0 is rawdata x-axis
 estimated_mu = np.log(scale)
 estimated_sigma = s
 
 print estimated_mu
 print estimated_sigma
 
 estimated mu = 1.4968829026551267
 estimated sigma = 0.8699922377581952

I am really sorry, for posting thiy wall of numbers, and clearly dumb beginner questions, but im quite desperate right now. Any help is appreciated!

Thx, Carol