integral

Given a Laplace Distribution proposal: g(x) = 1/2*e^(-|x|) and sample size n = 1000 , I want to Conduct the Monte Carlo (MC) integration for estimating θ: via importance sampling. Eventually I want to calculate the mean and standard deviation of this MC estimate in R once I get there. Edit (arrived late after the answer below) This is what I have for my R code so far: library(VGAM) n = 1000 x = rexp(n,0.5) hx = mean(2*exp(-sqrt(x))*(sin(x))^2) gx = rlaplace(n, location = 0, scale = 1) Now we can write a simple R function to sample from Laplace distribution: ## `n` is sample size rlaplace <-

I want to solve the following in R: ∫ 0 H [π( t ) ∫ t H A ( x ) dx ] dt Where π(t) is the prior and A(x) is the A function defined below. prior <- function(t) dbeta(t, 1, 24) A <- function(x) dbeta(x, 1, 4) expected_loss <- function(H){ integrand <- function(t) prior(t) * integrate(A, lower = t, upper = H)$value loss <- integrate(integrand, lower = 0, upper = H)$value return(loss) } Since π(t), A(x) > 0, expected_loss(.5) should be less than expected_loss(1). But this is not what I get: > expected_loss(.5) [1] 0.2380371 > expected_loss(1) [1] 0.0625 I'm not sure what I'm doing wrong. In your

I want to compute the following type of integrals in Matlab. It is the integral of function e^-(u)*u and the boundaries are zero and infinity. This integral should return 1. How can I do this in Matlab? And if you don't have the symbolic toolbox, or want more speed, quadgk supports infinite limits: f = @(x) x.*exp(-x); a = quadgk(f, 0, inf) a = 1.000000000000000e+00 Symbolic toolbox. syms u int(exp(-u)*u, u, 0, inf) 来源： https://stackoverflow.com/questions/11839394/infinite-integration-with-matlab

I'm having some problems with integration function in R. I'm trying to plot the integral vo but it seems I'm not doing correctly. t <- seq(0, 0.04, 0.0001) vi <- function(x) {5 * sin(2 * pi * 50 * x)} vo <- function(x) {integrate(vi, lower=0, upper=x)$value} test_vect = Vectorize(vo, vectorize.args='x') plot(t, vo(t)) # should be a cosine wave plot(t, vi(t)) # sine wave vo should be a sine wave but using test_vect gives me wrong plot and using vo directly gives error 'x' and 'y' lengths differ . Can anyone, please, help me on this matter? You are already there. Just use plot(t, test_vect(t)) .

I'm wondering how to code that takes double integrals in R. I already referred two similar questions. calculating double integrals in R quickly double integration in R with additional argument But I'm still confused how I can get my question from those answers. My question is following. I would like to code this calculations in R. From my hand and Wolfram alpha calculation, it becomes 16826.4. I know how to take a integral if both integrals are from exact numbers using adaptIntegrate(). But I'm not sure how to do in my case. Could you guys help me? Thank you so much in advance. Let me start