Timeline for How to plot this pdf?
Current License: CC BY-SA 4.0
13 events
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| Oct 12, 2020 at 3:36 | comment | added | user64494 | @JimB: That approach is primitive and misleading: the PDF in the case under consideration does not exist so it is impossible to plot it. That's all. | |
| Oct 12, 2020 at 1:33 | comment | added | JimB | @user64494. OK. I now understand (from an answer to stats.stackexchange.com/questions/491443/…) why what is being ask to plot is not a pdf. However, there does appear to be a few ways to plot something for this example that can give one an idea as to the shape of the distribution analogous to a pdf. | |
| Oct 11, 2020 at 5:40 | comment | added | user64494 | @JimB: BTW, the comment to your question on CrossValidated refers to an unknown math journal Information Visualization 2019, Vol. 18(3) 311–317. | |
| Oct 11, 2020 at 5:33 | comment | added | JimB | Thanks. I've gone ahead and asked the folks on CrossValidated: stats.stackexchange.com/questions/491443/…. | |
| Oct 11, 2020 at 5:27 | comment | added | user64494 | @JimB:: See Cantor distribution to this end. Don't hesitate to ask for further explanation in need. | |
| Oct 11, 2020 at 4:26 | comment | added | RandomBear | I was wondering how is the "density function" defined in such cases where there is a probability mass at a point and the CDF is differentiable at other points? | |
| Oct 9, 2020 at 16:23 | comment | added | JimB | Sorry, I was way too loose with my words. The PDF will exist at any point where the CDF is differentiable. And the PDF does not have to exist at every point to disallow the plotting of the PDF at the points where it does exist. In the OP's example, suppose the $\kappa$ is very small resulting in a very small probability mass at 0 but plotting the PDF where the PDF exists will still give an appropriate picture of the distribution of that random variable. However, I am unaware of a standard way to display the probability mass in such a situation other than including an explanatory note. | |
| Oct 9, 2020 at 5:22 | comment | added | user64494 | @JimB: Can you ground "However, there's no reason not to plot the PDF where the random variable is continuous"? I prefer arguments over empty words. | |
| Oct 9, 2020 at 4:42 | comment | added | JimB | In this case it's simpler to plot the CDF as it is defined everywhere. However, there's no reason not to plot the PDF where the random variable is continuous. In this case one would likely put a dot maybe at (0,0) and note that there's a probability mass of $\frac{1}{2} \left(\text{erf}\left(\frac{\log (\kappa )-\mu +1}{\sqrt{2} \sigma }\right)+1\right)$ at $y=0$ where $\kappa>0$. | |
| Oct 8, 2020 at 23:40 | comment | added | user64494 | This result makes no sense in traditional math since the integral for CDF through PDF makes no sense. The PDF exists only for absolutely continuous distributions (see encyclopediaofmath.org/wiki/Continuous_distribution and en.wikipedia.org/wiki/Probability_density_function ). Such approach leads to bugs e.g. as in mapleprimes.com/posts/207769-Bug-In-Probability. In order to calculate the mean and so on the Riemann-Stielttjes integral is used. | |
| Oct 8, 2020 at 3:25 | history | undeleted | AsukaMinato | ||
| Oct 8, 2020 at 3:24 | history | deleted | AsukaMinato | via Vote | |
| Oct 8, 2020 at 3:23 | history | answered | AsukaMinato | CC BY-SA 4.0 |