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Cleaned up the expected value notation.
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edit approved Feb 18, 2022 at 21:33
user476158
edit approved Feb 18, 2022 at 21:33
user476158

Laplace transform and fractional moments.

Is there any "easy" way to calculate fractional moments from Laplace transform. To be more specyfic let us consider the following example. Let $X$ be a positive random variable and $L(\theta) := E \exp (-\theta X)$$L(\theta) := E[\exp (-\theta X)]$ be its Laplace transform. Of course it is easy to calculate $E X^n$$E[X^n]$ where $n$ is a natural number but what with e.g. $E X^{1/2}$$E[ X^{1/2}]$.

Laplace transform and fractional moments.

Is there any "easy" way to calculate fractional moments from Laplace transform. To be more specyfic let us consider the following example. Let $X$ be a positive random variable and $L(\theta) := E \exp (-\theta X)$ be its Laplace transform. Of course it is easy to calculate $E X^n$ where $n$ is a natural number but what with e.g. $E X^{1/2}$.

Laplace transform and fractional moments

Is there any "easy" way to calculate fractional moments from Laplace transform. To be more specyfic let us consider the following example. Let $X$ be a positive random variable and $L(\theta) := E[\exp (-\theta X)]$ be its Laplace transform. Of course it is easy to calculate $E[X^n]$ where $n$ is a natural number but what with e.g. $E[ X^{1/2}]$.

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Piotr Miłoś
Piotr Miłoś
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Laplace transform and fractional moments.

Is there any "easy" way to calculate fractional moments from Laplace transform. To be more specyfic let us consider the following example. Let $X$ be a positive random variable and $L(\theta) := E \exp (-\theta X)$ be its Laplace transform. Of course it is easy to calculate $E X^n$ where $n$ is a natural number but what with e.g. $E X^{1/2}$.