You can’t. Both location and slope depends on alpha and beta.
You can see this by solving for example for y=0.5, and to differentiate to find the slope.
Stackoverflow cannot show math formulas [Latex], so formulas are given as images.
x value for y=0.5:
Slope at x=1:
EDIT: for completeness, here is the code to show the graphs:
import matplotlib.pyplot as plt
import numpy as np
def f[a,b,g,x]:
return 1 - [1 - g] * np.exp[-[[x/a]**b]]
x = np.linspace[0, 3, 100]
plt.figure[figsize=[4,3]]
for a in [0.5,1,1.5]:
y = f[a,2,0,x]
plt.plot[x,y]
plt.show[]
Statistics and Machine Learning Toolbox™ uses a two-parameter Weibull Distribution with a scale parameter a and a shape parameter b in the probability distribution object
WeibullDistribution and distribution-specific functions such as wblpdf and wblcdf. The Weibull distribution can take a third parameter. The three-parameter
Weibull distribution adds a location parameter that is zero in the two-parameter case. If X has a two-parameter Weibull distribution, then Y=X+c has a three-parameter Weibull distribution with the added location parameter c.
The probability density function [pdf] of the three-parameter Weibull distribution becomes
f[x|a,b,c]={ba[x- ca]b-1exp[-[x-ca]b]if x>c,0 if x≤c,
where a and b are positive values, and c is a real value.
If the scale parameter b is less than 1, the probability density of the Weibull distribution approaches infinity as x approaches c. The maximum of the likelihood function is infinite. The software might find satisfactory estimates in some cases, but the global maximum is degenerate when b