Timeline for Is it possible that two Random Variables from the same distribution family have the same expectation and variance, but different higher moments?
Current License: CC BY-SA 3.0
10 events
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| Aug 27, 2018 at 16:08 | comment | added | whuber♦ | @Martijn We're suffering from a badly phrased question, so making one's interpretation clear is important. I am focusing on the final statement, "But if the number of parameters is ≤2 and X and Y come from the same distribution family with the same expectation and variance, then does it mean that Z1 and Z2 has the same distribution (higher moments)?" That makes no reference to location-scale families. The answer to it is a definite no. If it were to be modified to stipulate that it is a location-scale family, then the answer is yes, assuming a standard meaning of "parameter." | |
| Dec 26, 2017 at 0:33 | comment | added | gioxc88 | I am sorry if I have not been very clear and I thank you for the time you have spent for looking into this but that is not what I asked. | |
| Dec 26, 2017 at 0:13 | comment | added | Carl | @whuber I congratulate you on your largess over a solitary interpretative approach. I wish this were more common. | |
| Dec 25, 2017 at 23:30 | comment | added | whuber♦ | @Carl After re-reading this answer, I need to retract my original assessment: this answer is correct (and +1 for that), and it is correct because it clearly explains how it is interpreting the original question. (Specifically, there is a common yet narrow concept of a "location-scale family" as consisting of just a single standard distribution along with all its translates and positive rescalings.) I believe the original question was intended to ask something a little different; the basis of that belief is the reference to more than two parameters in the post. | |
| Dec 25, 2017 at 23:27 | history | edited | whuber♦ | CC BY-SA 3.0 |
Prettified the TeX a little.
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| Dec 25, 2017 at 1:31 | comment | added | Carl | @whuber Please see my comments under Xi'an's answer. I do not agree with him but did not downvote because both he and you have a right to your opinion, even if I consider it to be incorrect. | |
| Dec 24, 2017 at 20:22 | comment | added | whuber♦ | @Carl This answer is incorrect--that's why it's being downvoted. Xi'an has already provided a counterexample. | |
| Dec 24, 2017 at 18:28 | comment | added | Carl | (+1) I cannot find fault with this answer. Apparently someone does, and they also find fault with mine. I do not understand this unexplained behaviour. | |
| Dec 24, 2017 at 3:34 | review | First posts | |||
| Dec 24, 2017 at 9:03 | |||||
| Dec 24, 2017 at 3:34 | history | answered | yyzz | CC BY-SA 3.0 |