Python log-normal distribution

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I’m trying to adjust the log-normal distribution to this data but I don’t know how to find the mean, standard deviation and adjust the Python distribution curve (I’m using Jupyter in Anaconda). I had already tried to do this with the normal distribution, but looking at the graph better, it seems that what fits the data more is a log-normal distribution rather than a normal one. Could you tell me how I can change the code and put a log-normal distribution instead of normal, please, for the same data set?

#amostra 22A
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import norm
import matplotlib.ticker as tkr
import scipy, pylab
import locale
locale.setlocale(locale.LC_NUMERIC, "de_DE")
plt.rcParams['axes.formatter.use_locale'] = True

df=pd.DataFrame({'frequencia_relativa': {'0-1': 0.282, '1-2': 0.316, '2-3': 0.171, '3-4': 0.068, '4-5': 0.085, '5-6': 0.026, '6-7': 0.026, '7-8': 0.009, '8-9': 0.009, '9-10': 0.0, '10-11': 0.0, '11-12': 0.009}})
df=df.reindex(['0-1', '1-2', '2-3', '3-4', '4-5', '5-6', '6-7',
       '7-8', '8-9', '9-10', '10-11', '11-12'])
plt.rcParams["figure.figsize"] = [15,8]
fig, ax =plt.subplots()
ax.bar(x=df.index, height=df.frequencia_relativa, alpha=0.5, width=0.9)
ax.set_xlabel('Tamanho lateral do triângulo ($\mu m$)', fontsize=22)
ax.set_ylabel('Frequência relativa', fontsize=22)
x_axis = np.arange(0, 10, 0.001)
plt.xticks(fontsize=18)
plt.yticks(fontsize=18)
#normal com média 2,232 e variância 1.88, conforme planilha
ax.plot(x_axis, norm.pdf(x_axis,2.232,1.888), linewidth=3)
#plt.show()
plt.savefig('output.png', dpi=500, bbox_inches='tight')

inserir a descrição da imagem aqui

python graphic

  • substitute norm for lognorm in the code. See documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html

  • @Lucas I’m not getting it. He’s giving me a strange graph. Maybe it’s because I don’t know how to calculate the new mean and standard deviation. How can I calculate that for this data set and distribution? Would you please put your hypothesis as an answer? Thank you so much for your patience and help, without you I wouldn’t be learning as much as I’ve been learning

1 answer

-2

Its variable X occurs at the midpoint of the classes, X=[0.5,1.5,2.5, etc...,11.5 ] - the distribution seems to be log normal with mean possibly in class 1.5 on this scale, but if it is even log normal, you should look for the mean in Ln(x).

Transform X into Ln(X); on this scale the distribution must be normal, but it will also be asymmetrical due to lack of histogram resolution (possibly by sub-sampling); hence you remove Ln(mean) and Ln(standard deviation), generates another vector Ln(X) more refined, calculates relative frequencies using the standard normal distribution in Z (mean zero, deviation 1) and takes this vector back to the space of its variable X using X = Exp(Ln(mean) + Z * Ln(standard deviation)).

Following this procedure I found mean of 0.67 and deviation of 2.59 in X. For this, I used trial and error, since optimization did not lead to good results. Note that in your modeling, the average is actually pointing to the standard deviation.

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