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YCor
YCor
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Michael Hardy
Michael Hardy
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I have a random variable $X \sim Gamma(\alpha, \beta)$$X \sim \operatorname{Gamma}(\alpha, \beta)$.

How can I compute or approximate $\mathbb{E} sin(X)$$\mathbb{E} \sin(X)$ very quickly? Iterative quadrature would be too slow, I need some closed form expression.

One idea I considered was to use the Gamma moments and Tyler approximation, but it would take too many terms, since $X$ has large standard deviation (in the order of 10-5010–50) and so the mass is not tightly concentrated.

I have a random variable $X \sim Gamma(\alpha, \beta)$.

How can I compute or approximate $\mathbb{E} sin(X)$ very quickly? Iterative quadrature would be too slow, I need some closed form expression.

One idea I considered was to use the Gamma moments and Tyler approximation, but it would take too many terms, since $X$ has large standard deviation (in the order of 10-50) and so the mass is not tightly concentrated.

I have a random variable $X \sim \operatorname{Gamma}(\alpha, \beta)$.

How can I compute or approximate $\mathbb{E} \sin(X)$ very quickly? Iterative quadrature would be too slow, I need some closed form expression.

One idea I considered was to use the Gamma moments and Tyler approximation, but it would take too many terms, since $X$ has large standard deviation (in the order of 10–50) and so the mass is not tightly concentrated.

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Todor Markov
Todor Markov
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Expected value of sin(X) for Gamma r.v. X in closed form (approximation is fine)

I have a random variable $X \sim Gamma(\alpha, \beta)$.

How can I compute or approximate $\mathbb{E} sin(X)$ very quickly? Iterative quadrature would be too slow, I need some closed form expression.

One idea I considered was to use the Gamma moments and Tyler approximation, but it would take too many terms, since $X$ has large standard deviation (in the order of 10-50) and so the mass is not tightly concentrated.