similar to: Help Regarding 'integrate'

I've written a series of functions that evaluates an integral from -inf to a or b to +inf using equally spaced quadrature points along a normal distribution from -10 to +10 moving in increments of .01. These functions are working and give very good approximations, but I think they are computationally wasteful as I am evaluating the function at *many* points. Instead, I would prefer to use

Hello to all, I am having trouble with intregrating a complicated uni-dimensional function of the following form Phi(x-a_1)*Phi(x-a_2)*...*Phi(x-a_{n-1})*phi(x-a_n). Here n is about 5000, Phi is the cumulative distribution function of standard normal, phi is the density function of standard normal, and x ranges over (-infty,infty). My idea is to to use quadrature to handle this integral. But

Dear R-users I would like to integrate something like \int_k^\infty (1 - F(x)) dx, where F(.) is a cumulative distribution function. As mentioned in the "integrate" help-page: integrate(dnorm,0,20000) ## fails on many systems. This does not happen for an adaptive Simpson or Lobatto quadrature (cf. Matlab). Even though I am hardly familiar with numerical integration the implementation

Hi, I would like to solve a double integral of the form \int_0^1 \int_0^1 x*y dx dy using Gauss Quadrature. I know that I can use R's integrate function to calculate it: integrate(function(y) { sapply(y, function(y) { integrate(function(x) x*y, 0, 1)$value }) }, 0, 1) but I would like to use Gauss Quadrature to do it. I have written the following code (using R's statmod package)

Hello all, I'm hoping to find a way to evaluate the following sort of integral in R. \int_a^b \int_{g(y)}^Inf f(x,y) dx dy. The integral has no closed form and so must be evaluated numerically. The "adapt" package provides for multidimensional integration but does not appear to allow the limits of integration to be a function. I need to evaluate a number of integrals of this

In the help for ?integrate: >When integrating over infinite intervals do so explicitly, rather than just using a large number as the endpoint. This increases the chance of a correct answer ? any function whose integral over an infinite interval is finite must be near zero for most of that interval. I understand that and there are examples such as: ## a slowly-convergent integral integrand

Dear list, [cross-posting from Stack Overflow where this question has remained unanswered for two weeks] I'd like to perform a numerical integration in one dimension, I = int_a^b f(x) dx where the integrand f: x in IR -> f(x) in IR^p is vector-valued. integrate() only allows scalar integrands, thus I would need to call it many (p=200 typically) times, which sounds suboptimal. The

Hi R users, I have a couple of questions about some problems that I am facing with regard to numerical integration and optimization of likelihood functions. Let me provide a little background information: I am trying to do maximum likelihood estimation of an econometric model that I have developed recently. I estimate the parameters of the model using the monthly US unemployment rate series

Hi All, I am trying to use A Gaussian quadrature over the interval (-infty,infty) with weighting function W(x)=exp(-(x-mu)^2/sigma) to estimate an integral. Is there a way to do it in R? Is there a function already implemented which uses such weighting function. I have been searching in the statmode package and I found the function "gauss.quad(100, kind="hermite")" which uses

Hi all, We know that Hermite polynomial is for Gaussian, Laguerre polynomial for Exponential distribution, Legendre polynomial for uniform distribution, Jacobi polynomial for Beta distribution. Does anyone know which kind of polynomial deals with the log-normal, Student抯 t, Inverse gamma and Fisher抯 F distribution? Thank you in advance! David [[alternative HTML version deleted]]

Dear all, This is the first time I am posting to the r-devel list. On StackOverflow, they suggested that the strange behaviour of integrate() was more bug-like. I am providing a short version of the question (full one with plots: https://stackoverflow.com/q/55639401). Suppose one wants integrate a function that is just a product of two density functions (like gamma). The support of the

Dear R list I am looking for a function in R that computes the integration of a discrete curve, such as a power spectrum, in a specified interval (in my case, that would be 'power in a certain frequency band'). I found only functions, such as 'integrate', that perform adaptive quadrature on analytic functions, and not on a curve specified as a set of (x,y) pairs. I have the

Dear list, I'm calculating the integral of a Gaussian function from 0 to infinity. I understand from ?integrate that it's usually better to specify Inf explicitly as a limit rather than an arbitrary large number, as in this case integrate() performs a trick to do the integration better. However, I do not understand the following, if I shift the Gauss function by some amount the integral

I am trying to test out several mgcv::gam models in a scalar-on-function regression analysis. The following is the 'hierarchy' of models I would like to test: (1) Y_i = a + integral[ X_i(t)*Beta(t) dt ] (2) Y_i = a + integral[ F{X_i(t)}*Beta(t) dt ] (3) Y_i = a + integral[ F{X_i(t),t} dt ] equivalents for discrete data might be: 1) Y_i = a + sum_t[ L_t * X_it * Beta_t ] (2) Y_i

Hi there, I am using SAS Proc NLMIXED to maximize a likelihood with multivariate normal random effects. An example is the two part random effects model for repeated measures semi-continous data with a cluster at 0. I use the "model y ~ general(loglike)" statement in Proc NLMIXED, so I can specify a general log likelihood function constructed by SAS programming statements. Then the

I need to compute a high dimensional integral. Currently I'm using the function adapt in R package adapt. But this method is kind of slow to me. I'm wondering if there are other solutions. Thanks. Zhongwen -- View this message in context: http://www.nabble.com/functions-for-high-dimensional-integral-tp17702978p17702978.html Sent from the R help mailing list archive at Nabble.com.

Hello: The example "integrate(dnorm,0,20000)" says it "fails on many systems". I just got 0 from it, when I should have gotten either an error or something close to 0.5. I got this with R 2.12.0 under both Windows Vista_x64 and Linux (Fedora 13); see the results from Windows below. I thought you might want to know. Thanks for all your work in creating

Dear all, I want to see the source codes for "dchisq(x, df, ncp=0, log = FALSE)", but cannot find it. I input "dchisq" in the R interface, and then enter, the following message return: > dchisq /*****************************************************/ function (x, df, ncp = 0, log = FALSE) { if (missing(ncp)) .Internal(dchisq(x, df, log)) else

Hello, I want to know if there are some functions or packages to solve differential and integral equation using R. Thanks. Shao chunxuan. [[alternative HTML version deleted]]

I believe this may be more related to analysis than it is to R, per se. Suppose I have the following function that I wish to integrate: ff <- function(x) pnorm((x - m)/sigma) * dnorm(x, observed, sigma) Then, given the parameters: mu <- 300 sigma <- 50 m <- 250 target <- 200 sigma_i <- 50 I can use the function integrate as: > integrate(ff, lower= -Inf, upper=target)