we we're asked about it, and I know that answer is "NO", and I haven't found an good enough answer yet and would appreciate an explanation with examples.
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1Duplicate of : https://mathoverflow.net/questions/3525/when-are-probability-distributions-completely-determined-by-their-moments – kjetil b halvorsen Mar 14 '21 at 17:16
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1Does this answer your question? When are probability distributions completely determined by their moments? – Will Sawin Mar 15 '21 at 01:54
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An example, and a necessary and sufficient condition (in the case when the distribution is absolutely continuous) for the uniqueness, can be found e.g. here.
Iosif Pinelis
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