Does there exist a probability distribution such that all central moments are equal?

Asked Dec 05 '19 at 02:45

Active Dec 05 '19 at 02:45

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I find here that if the moment generating function of a random variable has positive radius of convergence, then that random variable is determined by its moments. So does there exist a continuous probability distribution on $\mathbb R$ such that all of its moments are equal?

It is a bit tricky because saying that random variable is determined by its moments is not the same as saying that given any sequence of moments a random variable can be found.

asked Dec 05 '19 at 02:45

Ma Joad

7,696

Moments (as in the body of your question) or central moments (as in the title)? – kimchi lover Dec 05 '19 at 02:58
Similar: https://math.stackexchange.com/q/2404117/578053 – Dec 05 '19 at 03:00

Does there exist a probability distribution such that all central moments are equal?

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