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I have a set of insurance data. Development factors Development factors fall with period, so follow Weibull distribution. I want to estimate Weibull parameters and smooth Development Factors. If I estimate parameters of Weibull using fitdistr() code in R I get shape parameter = 0.9567142 and scale parameter = 1.8321954. With this parameters I want to smooth the Development Factors given x-values equal to Period, but this gives me very low numbers. So for Period = 1 and these parameters, it returns 0.3061, which is way lower than original 20.27199. What am I doing wrong? Thank you in advance

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    $\begingroup$ 1. While development factors "fall" that doesn't make them Weibull; in fact they cannot be a multiple of a Weibull density because they converge to 1 (from above) while a Weibull density converges to 0. 2. fitdistr works on random samples from a distribution, not from density or cdf values. 3 You also cannot reasonably use nonlinear least squares to fit some curve to the development factors since development factor values are highly dependent and strongly heteroskedastic. $\endgroup$
    – Glen_b
    Jan 14, 2019 at 13:07

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If it might be of some use, I got an OK fit to factor as a function of period using an exponential equation with offset, "factor = a * exp(b * period) + Offset", with parameters a = 1.2148647556770337E+02, b = -1.8447383394431971E+00, and Offset = 1.0678593236739169E+00 yielding R-squared = 0.9997 and RMSE = 0.0876.

plot

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