Timeline for The connection between a random variable's moments and its tails
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 28, 2015 at 0:12 | comment | added | user78229 | @AlmostShirley Maybe it makes sense. Do you understand that distributional assumptions about a random variate are rarely fixed and that multiple distributions can be made to fit the same information? What attributes or characteristics do you associate with "exponential tails" that make them so desirable? | |
| Oct 27, 2015 at 23:15 | comment | added | Almost Shirley | @DJohnson Because I have a random variable that I hope has exponential tails, but for which I ONLY have information about the tails. I know that they are finite. And I know something about how they grow. I thought understanding how this would be possible with the normal distribution might give me some insight into the general case, so I could apply it to my not-well understood random variable. Make sense? | |
| Oct 27, 2015 at 21:54 | comment | added | user78229 | @AlmostShirley I don't want to seem impertinent but why are you so concerned with exponential tails? What is driving this...for want of a better word...obsession? For instance, consider this Wiki discussion of natural exponential families of distributions... en.wikipedia.org/wiki/Natural_exponential_family | |
| Oct 27, 2015 at 21:31 | comment | added | Almost Shirley | Sure, that makes sense. But perhaps we can't know that the tails are exponential. Seems like a subtle question. | |
| Oct 27, 2015 at 18:41 | comment | added | whuber♦ | Yes, of course. For instance, it immediately implies the tails are not powers. | |
| Oct 27, 2015 at 16:22 | comment | added | Almost Shirley | But I am asking about the other direction. I have knowledge of all the moments. Suppose they are all finite. Can we say anything about the tails? | |
| Oct 27, 2015 at 16:12 | comment | added | whuber♦ | The existence of an infinite moment implies at least one tail is "fatter" than exponential--and provides quantitative information about its decay rate. | |
| Oct 27, 2015 at 15:02 | history | edited | Nick Cox | CC BY-SA 3.0 |
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| Oct 27, 2015 at 15:02 | comment | added | user78229 | Nope...not as far as I'm aware...but I will defer to others on this one... | |
| Oct 27, 2015 at 14:59 | comment | added | Almost Shirley | I KNOW that the normal distribution has exponential tails. I am asking if you can understand this from just looking at the moments. | |
| Oct 27, 2015 at 14:58 | comment | added | user78229 | The normal distribution is a member of the family of exponential distributions. Does that answer your question? | |
| Oct 27, 2015 at 14:42 | comment | added | Almost Shirley | So it can be proved that because the normal distribution has finite moments that it has exponential tails? Do you have an argument or a link to one? | |
| Oct 27, 2015 at 14:39 | history | answered | user78229 | CC BY-SA 3.0 |