For a positive random variable, does the function $$ G\colon [0,\infty)\to [0,\infty]\\ G(\lambda):=\mathbb{E}[X^{\lambda}] $$ have a name?
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The $\lambda$th moment? – David G. Stork Mar 06 '18 at 19:16
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1For each value of $\lambda$ we may call it the fractional moment of $X$. Or we may also consider it as the moment generating function of $\log X$. But I am not sure whether a specific name for $G$ is assigned in function viewpoint. – Sangchul Lee Mar 06 '18 at 19:17
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@DavidG.Stork but im talking about the function, not just its value at one point – Bananach Mar 06 '18 at 19:22
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@SangchuiLee Thats exactly what I was looking for, I was dumb for not realizing that connection myself – Bananach Mar 06 '18 at 19:23