Determine Weibull parameters from data

Question

I would like to identify the Weibull parameters (i.e. the shape and scale) of my data.

0.022988506
0.114942529
0.218390805
0.114942529
0.149425287
0.114942529
0.068965517
0.068965517
0.034482759
0.022988506
0.022988506
0.022988506
0.022988506

I've already tried what this answer proposed, and I'm using Python 3.4.

import scipy.stats as s
import numpy as np
from scipy import stats


def weib(x,n,a):
    return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)


data = np.loadtxt("data1.csv")
print(data)
(loc, scale) = s.exponweib.fit_loc_scale(data, 1, 1)
print('loc is: ',loc, '\n scale is: ', scale)

This gives me the following output:

[0.02298851  0.11494253  0.2183908   0.11494253  0.14942529  0.11494253   0.06896552  0.06896552  0.03448276  0.02298851  0.02298851  0.02298851 0.02298851]
loc is:  0.0574417296258 
scale is:  0.0179259738449

I assume that the data in my csv file was read as x-input values, instead of the y-values of the Weibull function. When I add a second column (or row) with bin, it gives an error that string values can not be converted into floats.

How do I need to modify my csv file in order to use the data within as the y-values of the Weibull function?

I think my problem might be that I don't understand this line:

(loc, scale) = s.exponweib.fit_loc_scale(data, 1, 1)

What does 1, 1 represent here? The parameters should then not be negative.

Answer 1

It looks like you want to use the fit method of scipy.stats.weibull_min (which is an alias for scipy.stats.frechet_r). Use the argument floc=0 to constrain the location to be 0.

In [9]: data
Out[9]: 
array([ 0.02298851,  0.11494253,  0.2183908 ,  0.11494253,  0.14942529,
        0.11494253,  0.06896552,  0.06896552,  0.03448276,  0.02298851,
        0.02298851,  0.02298851,  0.02298851])

In [10]: from scipy.stats import weibull_min

In [11]: shape, loc, scale = weibull_min.fit(data, floc=0)

In [12]: shape
Out[12]: 1.3419930069121602

In [13]: scale
Out[13]: 0.084273047253525968