Integrals simulation in the program R

by Sajjad Esmaili   Last Updated May 16, 2019 06:19 AM

let $x|\lambda \sim exp (\lambda) \to \lambda | x \sim \Gamma(2,x)$ , $L(\theta , a)=(\theta-a)^2$ , $\theta=\lambda\to $$E^{\pi}(\theta)=2/\pi$

if $L(\theta -a)=|\theta-a|, p(theta \leq \sigma^{\pi}(x)|x)=1/2$ not that $f(\lambda | x) = x^2 \lambda e^{- \lambda x}$ with a numberic appaocch find $\sigma^{\pi}$ shoche that $\int_0^{\sigma^\pi (x)} x^2 \lambda e^{-\lambda x} d x =1/2$ I want this integral to simulate



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