Have you ever wondered if your Weibull PDF is a good fit for your data? I recently came across a question on Reddit where someone was struggling to determine if their Weibull distribution was correctly fitted. They were using Python SciPy’s `weibull_min` function, which requires a shape parameter to calculate the scale and shift automatically. But how do you know if the resulting PDF is a good fit?
One way to check is by visually inspecting the PDF. If the curve looks like a bell shape, it might be a good indication that the fit is correct. However, this method is not foolproof and can be subjective. A better approach would be to use numerical methods to evaluate the goodness of fit.
One such method is the Kolmogorov-Smirnov test, which compares the empirical distribution function of the data with the theoretical distribution function of the Weibull distribution. If the test statistic is below a certain threshold, you can reject the null hypothesis that the data comes from a Weibull distribution.
Another approach is to use maximum likelihood estimation to estimate the parameters of the Weibull distribution and then evaluate the fit using metrics such as the Akaike information criterion (AIC) or the Bayesian information criterion (BIC).
In conclusion, determining if a Weibull PDF is a good fit requires a combination of visual inspection and numerical methods. By using these techniques, you can increase your confidence in the accuracy of your results.