similar to: Bivariate normal integral

Dear list members I need a function that calculates the bivariate normal distribution for each observation. It is part of a likelihood function and I have 1000's of cases. As I understand it I cannot use packages like "mvtnorm" because it requres a covariance matrix of the same dimension as the number of observations. Basically what I need is a function that takes as arguments a

Package mvtnorm provides dmvnorm, pmvnorm that can be used to compute Pr(X=x,Y=y) and Pr(X<x,Y<y) for a bivariate normal. Are there functions that would compute Pr(X<x,Y=y)? I'm currently using "integrate" with dmvnorm but it is too slow.

Suppose F(x, y; rho) is the cdf of a bivariate normal distribution, with standardized marginals and correlation parameter rho. For any fixed x and y, I wonder if F(x, y; rho) is a monotone increasing function of rho, i.e., there is a 1 to 1 map from rho to F(x, y; rho). I explored it using the function pmvnorm in package mvtnorm with different x and y. The plot suggests the statement may be true.

Dear all, I am trying to calculate certain critical values from bivariate normal distribution (please see the function below). m <- 10 rho <- 0.1 k <- 2 alpha <- 0.05 ## calculate critical constants cc_z <- numeric(m) var <- matrix(c(1,rho,rho,1), nrow=2, ncol=2, byrow=T) for (i in 1:m){ if (i <= k) {cc_z[i] <- qmvnorm((k*(k-1))/(m*(m-1))*alpha,

I'm trying to implement a recursive function using integrate, and I suspect I need a Vectorize somewhere, but I can't suss it out. Any help would be appreciated. I've tried traceback() and various debugging ideas to no avail (most likely due to my inexperience with these tools.) Here's what I have. Nk <- function(m, C) { if (length(m) > 1) { rho <- C[1, -1]

Hello, I'm quite new with R and so I would like to know if there is a command to calculate an integral. In particular I simulated a bivariate normal distribution using these simple lines: rbivnorm <- function(n, # sample size mux, # expected value of x muy, # expected value of Y sigmax, # standard deviation of

hello I work on the probabilities of bivariate normal distribution. I need integrate  the following function. f (x, y) = exp [- (x ^ 2 + y ^ 2 + x * y)] with - ∞ ≤ x ≤ 7.44 and - ∞ ≤ y ≤ 1.44   , either software R or  matlab Version R 2009a Thank you for helping me Regards Mezouara hicham PhD in Metrology Hicham_dess @ yahoo.fr [[alternative HTML version deleted]]

Hi, can anyone help me with the following code? Thanks! library(mvtnorm) f2 <- function(n, rho) { var <- matrix(c(1,rho,rho,1), nrow=2, ncol=2, byrow=T) beta <- seq(0, 1, length.out=n+1) alpha <- sort (sapply(1-beta, qnorm)) x <- array(0, dim=c(n, n)) for (s in 1:n) { for (t in 1:n){ if (s>=t) x[s,t] <- pmvnorm(lower=c(alpha[s],

R-Help I am attempting to create a series of bivariate normal distributions. So using the mvtnorm library I have created the following code ... # Standard deviations and correlation sig_x <- 1 sig_y <- 1 rho_xy <- 0.0 # Covariance between X and Y sig_xy <- rho_xy * sig_x *sig_y # Covariance matrix Sigma_xy <- matrix(c(sig_x ^ 2, sig_xy, sig_xy, sig_y ^ 2), nrow = 2, ncol = 2)

Dear All I want to generate variable with Bivariate Normal Distribution by use mean1 = a, variance1 = b, mean2 = c, variance2 = d, rho = e. How I can do this. Many Thanks. IRD [[alternative HTML version deleted]]

Suppose I know the value of cumulative bivariate standard normal distribution. How can I solve correlation between variables? Pekka --------------------------------- [[alternative HTML version deleted]]

Hi. Does anyone know whether the following error is a result of a bug or a feature? I can eliminate the error by making ML=F, but I would like to see the values of the cut-points and their variance. tmp.vec<-c(0, 0, 0 , 0 ,0 , 1, 0, 2, 0 , 0, 5 ,5 ,3 ,1, 0 , 1, 5, 10, 27, 20, 9, 0, 1, 1, 12, 29, 57, 34, 0, 0, 1, 2, 11, 31, 32) tmp.mat<-matrix(tmp.vec, nrow=7)

Dear R-Users I would like to estimate a constrained bivariate normal density, the constraint being that the means are of equal magnitude but of opposite signs. So I need to estimate four parameters: mu (meanvector (mu,-mu)) sigma_1 and sigma_2 (two sd deviations) rho (correlation coefficient) I have looked at several packages, including Gaussian mixture models in Mclust, but I am not sure

I'm trying to obtain numerical derivative of a probability computed with mvtnorm with respect to its parameters using grad() and jacobian() from NumDeriv. To simplify the matter, here is an example: PP1 <- function(p){ thetac <- p thetae <- 0.323340333 thetab <- -0.280970036 thetao <- 0.770768082 ssigma <- diag(4) ssigma[1,2] <- 0.229502120

HI Guys, I know that this forum is not for homework but I am trying to interpret R output code. I was just wondering if someone might be able to help. I have been given the following. For (X1,X2) distributed bivariate normal with parameters mu1 = 5.8 mu2 = 5.3 sd1 = sd2 = 0.2 and p = 0.6 The r-code and inpit/output are as follows input m <- 5.3 + 0.6*(6.3 - 5.8) s <-

Hello, currently I'm working on a model based on Monte-Carlo-Simulations. I observed that a generated normal distributed times series using rnorm(100,mean=0,sd=1) is far away from being not autocorrelated. Is there any other gerenator implemented in R, which might solve my problem? -- View this message in context:

Hi, Let f(rho) = E[F_1(x) F_2(y)], i.e f(rho) is the expectation of F(x) * F(y) with respect to the bivariate Gaussian density with mean 0 and covariance matrix [1 rho; rho 1]. Moreover, assume F_1(x) and F_2(y) to be increasing functions of x and y respectively. I was wondering if it was true that f(rho) is an increasing function of rho. If so, are there any references? Best, Agos

Hi, R Users; I am trying to maximize a likelihood function which contains an integral. The integral contains the unknown parameter as well. I am trying to use the following code to do the maximization: ll<-function(b.vec){ b0<-b.vec[1] b1<-b.vec[2] b2<-b.vec[3] p<-1/(1+exp(-b0-b1*z1-b2*x2))

About two years ago there was a thread about this which suggested that at that time nobody had these coefficients ready to go. (a) has anyone in the meanwhile programmed them? (b) I think I can see how to do the tetrachoric one with mvtnorm on similar lines to an example on the help page so will try that if nobody else already has (c) looking at the polychoric one makes me realise yet again

Hi, I draw a surface corresponding to bivariate density of independent variables (rho=0) using persp(). Then I add a contour line (i.e., circle in my case) at a particular density. Below is a minimal example of what I have so far. # Bivariate density dnorm2d <- function(x, y, rho = 0) { xoy = (x^2 - 2 * rho * x * y + y^2)/(2 * (1 - rho^2)) density = exp(-xoy)/(2 * pi * sqrt(1 - rho^2))