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Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.
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Higher Moments of an Unknown Density Function
Look into Pearson distribution. This family is reach enough so that every 4-tuple of moments $m_1$, $m_2$, $m_3$ and $m_4$ corresponds to a unique (up to equivalence) member of the family.
Here is th …