Timeline for The relationship between the gamma distribution and the normal distribution
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 31, 2018 at 14:39 | answer | added | Sextus Empiricus | timeline score: 4 | |
| Mar 3, 2018 at 7:59 | comment | added | Carl | The connection is not mysterious, it is because they are members of the exponential family of distributions the salient property of which is that they can be arrived at by substitution of variables and/or parameters. See longer answer below with examples. | |
| Feb 28, 2018 at 10:54 | comment | added | Ben | While these results are well-known in the field of probability and statistics, well done to you @timxyz for rediscovering them in your own analysis. | |
| Feb 28, 2018 at 3:25 | answer | added | Carl | timeline score: 26 | |
| Nov 4, 2014 at 19:50 | vote | accept | timxyz | ||
| Nov 3, 2014 at 22:38 | comment | added | whuber♦ | Since Wikipedia defines the chi-squared distribution as a sum of squared Normals at en.wikipedia.org/wiki/Chi-squared_distribution#Definition and mentions the chi-squared is a special case of the Gamma (at en.wikipedia.org/wiki/Gamma_distribution#Others), one can scarcely claim these relationships are not well known. The variance itself merely establishes the unit of measurement (a scale parameter) in all cases and so introduces no additional complication at all. | |
| Nov 3, 2014 at 22:28 | answer | added | Alecos Papadopoulos | timeline score: 25 | |
| Sep 26, 2012 at 21:01 | history | tweeted | twitter.com/#!/StackStats/status/251063871798927360 | ||
| Sep 18, 2012 at 10:14 | comment | added | timxyz | I'm from a computer vision background so don't normally encounter the probability theory. None of my textbooks (or Wikipedia) mention this interpretation. I suppose I'm also asking, what's special about the sum of the square of two normal distributions that makes it a good model for waiting time (i.e. the exponential distribution). It still feels like I'm missing something deeper. | |
| Sep 18, 2012 at 1:02 | comment | added | Dilip Sarwate | Many undergraduate textbooks on probability theory mention all the above results; but perhaps statistics texts do not cover these ideas? In any case, a $N(0,\sigma^2)$ random variable $Y_i$ is just $\sigma X_i$ where $X_i$ is a standard normal random variable, and so (for iid variables) $\sum_i Y_i^2 = \sigma^2 \sum_i X_i^2$ is simply a scaled $\chi^2$ random variable is not surprising to those who have studied probability theory. | |
| Sep 18, 2012 at 0:40 | review | First posts | |||
| Sep 25, 2012 at 17:22 | |||||
| Sep 18, 2012 at 0:38 | history | asked | timxyz | CC BY-SA 3.0 |