I am new to Python and statistics, and I have a problem.
I have a random variable X whose values fall under a three-parameter lognormal distribution. I would like to plot the PDF of my variable.
X contains 500 samples (N=500), which are the following:
X = [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 36, 36, 36, 36, 36, 37, 38, 38, 39, 39, 40, 42, 42, 43, 43, 44, 45, 47, 48, 49, 49, 50, 50, 51, 52, 52, 54, 54, 55, 58, 62, 67, 67, 73, 80]
and the mean and standard deviation are:
Mean = 15.088
Stddev = 12.445
I have been doing some research, and I think the following code could be adapted to get the lognormal curve that I need with my data, but I do not understand very much how to do it, because I do not really comprehend how this distribution works.
The code is this:
from scipy import stats
import numpy as np
import matplotlib.pyplot as plt
import math
def lognorm(mu,variance):
size = 500
sigma = math.sqrt(variance)
np.random.seed(1)
gaussianData = stats.norm.rvs(loc=mu, scale=sigma, size=size)
logData = np.exp(gaussianData)
shape, loc, scale = stats.lognorm.fit(logData, floc=0)
logData.sort()
return logData, stats.lognorm.pdf(logData, shape, loc, scale)
x, y = lognorm(37, 0.8)
plt.plot(x, y)
plt.grid()
plt.show()
Any help with be much appreciated.
I have a random variable Words per sentence which contains those values:
words_per_sentence = [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 36, 36, 36, 36, 36, 37, 38, 38, 39, 39, 40, 42, 42, 43, 43, 44, 45, 47, 48, 49, 49, 50, 50, 51, 52, 52, 54, 54, 55, 58, 62, 67, 67, 73, 80]
The observation space contains 500 values (N=500), and the mean and standard deviation are:
mu = 15.088
sigma = 12.445
I want to calculate a three-parameters-lognormal PDF for my variable and plot it in a graph but I do not get the result I want. This is my failing code up to now:
import math
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
data = [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 36, 36, 36, 36, 36, 37, 38, 38, 39, 39, 40, 42, 42, 43, 43, 44, 45, 47, 48, 49, 49, 50, 50, 51, 52, 52, 54, 54, 55, 58, 62, 67, 67, 73, 80]
plt.hist(data, bins=50, color='c', alpha=0.75)
xmin = min(data)
xmax = max(data)
x = np.linspace(xmin, xmax, 200)
pdf = stats.lognorm.pdf(x, s=12.445, loc=1, scale=math.exp(15.088))
plt.plot(pdf, 'y')
The problem is that I do not get the PDF printed but a straight horizontal line in at the bottom of the graph. I cannot post any picture as I have not yet enough punctuation. Please help.
The character class you have there does not allow spaces. Add a space to it:
^[A-ZÑÁÉÍÓÚÜ ]+:
(Edited to add the Ñ that it needs)
Use
^[\p{Lu}\s]+:
See regex proof.
EXPLANATION
NODE EXPLANATION
--------------------------------------------------------------------------------
^ the beginning of the string
--------------------------------------------------------------------------------
[\p{Lu}\s]+ any character of: Unicode uppercase letter (\p{Lu}),
whitespace (\n, \r, \t, \f, and " ")
(1 or more times (matching the most amount possible))
--------------------------------------------------------------------------------
: ':'</pre>
If it does not work use
^[^:\r\n]+:
EXPLANATION
NODE EXPLANATION
--------------------------------------------------------------------------------
^ the beginning of the string
--------------------------------------------------------------------------------
[^:\r\n]+ any character except: ':', '\r' (carriage
return), '\n' (newline) (1 or more times
(matching the most amount possible))
--------------------------------------------------------------------------------
: ':'
I have the following data and after plotting scatter data point, I would like to add boxplot around each set of position. Here is my code for plotting the scatter plot:
%matplotlib inline
import matplotlib.pyplot as plt
X = [1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2,
3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4,
5, 5, 5, 5, 5, 5, 5,
6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7,
8, 8, 8, 8, 8, 8, 8,
9, 9, 9, 9, 9, 9, 9,
10, 10, 10, 10, 10, 10, 10,
11, 11, 11, 11, 11, 11, 11,
12, 12, 12, 12, 12, 12, 12,
13, 13, 13, 13, 13, 13, 13,
14, 14, 14, 14, 14, 14, 14,
15, 15, 15, 15, 15, 15, 15]
H = [15, 17, 16, 20, 15, 18, 15,
17, 16, 16, 20, 19, 18, 15,
20, 22, 20, 22, 19, 21, 21,
19, 21, 20, 23, 21, 20, 22,
21, 23, 22, 20, 24, 22, 20,
20, 19, 20, 18, 21, 17, 19,
18, 20, 16, 15, 17, 20, 19,
19, 19, 18, 21, 21, 16, 19,
21, 22, 22, 24, 24, 23, 25,
28, 26, 30, 27, 26, 29, 30,
27, 26, 29, 31, 27, 29, 30,
25, 26, 27, 28, 25, 27, 30,
31, 28, 25, 27, 30, 25, 31,
28, 26, 30, 28, 29, 27, 31,
24, 26, 25, 28, 26, 23, 25]
fig, axes = plt.subplots(figsize=(8,5))
axes.scatter(X, H, color='b')
axes.set_xlabel('Pos');
axes.set_ylabel('H, µm');
when i add plt.boxplot, it captures all data not individual position. I appreciate the answers either in matplotlib or seaborn.
thanks
A good way would be using pandas:
df = pd.DataFrame({'X':X, 'H': H})
ax=df.plot(kind='scatter', x='X', y='H')
df.boxplot(by='X', ax=ax)
plt.show()
output:
Here's a condensed solution to how to map your H array by X and plot it using matplotlib:
groups = [[] for i in range(max(X))]
[groups[X[i]-1].append(H[i]) for i in range(len(H))]
plt.boxplot(groups)
Outcome:
you can add grid with plt.grid(True)