Curve Fitting Tool - Weibull distribution
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I am trying to do a fitting of a graph, using the curve fitting Tool and, in particular, using the Weibull option that use the formula:
Despite the fact that the shape of the Weibull distribution seems to be the same of the one of my graph, the height of the Weibull distribution is lower. I have tried to calculate the integral of the Weibull function of the curve fitting tool of some data and the result is always 1. I think that this is due to the fact that it is a density function. With the above mentioned formula, it is impossible to fit properly the dataset because the Weibull distribution is always lower.
I used the approach shown here https://it.mathworks.com/help/curvefit/weibull.html, using the formula:
Using this approach I have seen that the parameter c helps to scale the data. Is this approach correct? The second formula that I used should not substitute the first one that is used as default in the curve fitting tool?
if I want to obtain a Weibull distribution or a Lognormal distribution is it sufficient to apply a multiplier coefficient (e.g. the c parameter, which is necessary in the formula above to allow the curve's height to adjust to data) to a density function?