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 Jun11 accepted Power Law Probability Distribution From Observations Jun4 comment Power Law Probability Distribution From Observations On second thought, am I misinterpreting the issue. It's not that I calculate $$P(x)$$ and then fit a power law but rather attempt to fit a power law distribution $$P(x) \propto x^\alpha$$ and then determine the accuracy of the fitted distribution. Is that the correct procedure? Jun4 asked Power Law Probability Distribution From Observations Sep17 awarded Supporter Sep14 comment Integrating $\int_0^{500}e^{\frac{(x-a)^2}{b^2}} dx$ Thanks for your detailed description of \Phi . I have been having trouble understanding how to use it and the most of the descriptions I have found about it go over my head slightly. I think I have a better idea of what to do now. Sep14 revised Integrating $\int_0^{500}e^{\frac{(x-a)^2}{b^2}} dx$ added 2 characters in body Sep14 comment Integrating $\int_0^{500}e^{\frac{(x-a)^2}{b^2}} dx$ There should indeed be a minus sign. The reason I omitted much of the detail is because I thought I could get a general understanding of the issue at hand and then apply it to my problem but it seems this issue is far more complex than I estimated. Sep14 comment Integrating $\int_0^{500}e^{\frac{(x-a)^2}{b^2}} dx$ Thanks again vanna. I thought maybe there was a way to calculate it, but if not then I will look more carefully into using a cdf. Sep14 awarded Editor Sep14 comment Integrating $\int_0^{500}e^{\frac{(x-a)^2}{b^2}} dx$ Ooops forgot those. . Edited Sep14 revised Integrating $\int_0^{500}e^{\frac{(x-a)^2}{b^2}} dx$ added 16 characters in body Sep14 awarded Student Sep14 asked Integrating $\int_0^{500}e^{\frac{(x-a)^2}{b^2}} dx$ Sep14 awarded Scholar Sep14 accepted Transforming a Continuous Function Sep14 comment Transforming a Continuous Function This is helping me greatly. Thank you. Could you recommend any reading material on normalizing functions. I am particularly interested in how you managed to calculate $$y(x) = \frac{1}{\phi\left(\frac{500-d}{c}\right)-\phi\left(\frac{-d}{c}\right)}\frac{1}‌​{c\sqrt{2\pi}}e^{-\frac{1}{2}\frac{(x-d)^2}{c^2}} 1_{\{0\le x \le 500\}}$$ Sep14 comment Transforming a Continuous Function Yes you right. My mistake. I just copied the formula directly without thinking. Sep14 comment Transforming a Continuous Function So if I calculate: $y(x) = \frac{1}{\int_0^500 b + \frac{a}{c\sqrt{\frac{\pi}{2}}} \cdot e^{\frac{-2(u-d)^{2}}{c^{2}}} du} \cdot (b + \frac{a}{c\sqrt{\frac{\pi}{2}}} \cdot e^{\frac{-2(x-d)^{2}}{c^{2}}})$ I can normalize the function yes? Also since the integral is between 0 and 500 that means that my x values will be bounded? Final question does this mean that I will be able to change the standard deviation and still maintain a curve with an approximately consistent area below the curve? Thank you very much for your clear and concise answer Sep14 asked Transforming a Continuous Function