search for: int_0

Dear all, I would be very grateful if you could help me with: Given the regularized gamma function Reg=int_0^r (x^(k-1)e^(-x))dx/int_0^Inf (x^(k-1)e^(-x))dx ; 0<r<Inf (which is eventually the ratio of the Incomplete gamma function by the gamma function), does anyone know of a package in R that would evaluate the derivative of the inverse of Reg with respect to k? I am aware that the function "R...

...f defined by f<-function(x,y,z) c(x,y^2,z^3) Thus, f is actually corresponding to three uni-dimensional functions f_1(x)=x, f_2(y)=y^2 and f_3(z)=z^3. What I am looking for are the integrals of these three functions f_1,f_2,f_3 over some interval, say, (0,1). More specifically, the integrals \int_0^1 f_1(x) dx, \int_0^1 f_2(y) dy and \int_0^1 f_3(z) dz. For this simple example, of course we can do these three integrals one by one using integrate (f_1, lower=0, upper=1) However, in practice, I have a sequence of 5000 uni-dimensional functions and hope to find all of their integrals (over s...

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...

...or those interested, I added this to the beginning of the \details{} section: \if{html}{\out{ <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax at 3/es5/tex-mml-chtml.js"> </script> }} And then I can use: \if{html}{\out{\(B_{x(a,b)} = \int_0^x t^{a-1} (1-t)^{b-1} dt\)}} or \if{html}{\out{\[B_{x(a,b)} = \int_0^x t^{a-1} (1-t)^{b-1} dt\]}} to render the equation (inline or as 'displaymath'). I'll try to add MathJax locally next. Best, Wolfgang >-----Original Message----- >From: Duncan Murdoch [mailto:murdoch.duncan...

...;beginning of the \details{} section: > >\if{html}{\out{ ><script id="MathJax-script" async >?? src="https://cdn.jsdelivr.net/npm/mathjax at 3/es5/tex-mml-chtml.js"> ></script> >}} > >And then I can use: > >\if{html}{\out{\(B_{x(a,b)} = \int_0^x t^{a-1} (1-t)^{b-1} dt\)}} > >or > >\if{html}{\out{\[B_{x(a,b)} = \int_0^x t^{a-1} (1-t)^{b-1} dt\]}} > >to render the equation (inline or as 'displaymath'). I'll try to add MathJax >locally next. > >Best, >Wolfgang > >>-----Original Message-----...

Hi, I need to integrate a 2D function over range where the limits depend on the other e.g integrate f(x,y)=x*y over {x,0,1} and {y,x,1}. i.e \int_0^1 \int_x^1 xy dydx I checked adapt but it doesn't seem to help here. Are they any packages for this sort of thing? I tried RSitesearch but couldn't find the answer to this. Many thanks for you help. Regards Saptarshi Saptarshi Guha | sapsi@pobox.com | http://www.stat.purdue.edu/~sg...

...or those interested, I added this to the beginning of the \details{} section: \if{html}{\out{ <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax at 3/es5/tex-mml-chtml.js"> </script> }} And then I can use: \if{html}{\out{\(B_{x(a,b)} = \int_0^x t^{a-1} (1-t)^{b-1} dt\)}} or \if{html}{\out{\[B_{x(a,b)} = \int_0^x t^{a-1} (1-t)^{b-1} dt\]}} to render the equation (inline or as 'displaymath'). I'll try to add MathJax locally next. Best, Wolfgang >-----Original Message----- >From: Duncan Murdoch [mailto:murdoch.duncan...

...having some difficulty getting a model specified for nls though. The math for the model that I want to fit is dg(t)/dt = K1 f(t) - k2 g(t) where g(t) and f(t) are measured data at a sequence of times t. K1 and k2 are the parameters of the model. If I solve this, the solution is g(t) = K1 \int_0^t f(t') \exp(-k2(t-t')) dt' and I'm not sure how to write a formula in R that I can pass to nls that will handle both the implicit loop over the data values of t and the interpolation and numeric integration over t'. Can anyone help me to get this properly coded for R? Mike...

I am trying to solve an integral in R. However, I am getting an error when I am trying to solve for that integral. The equation that I am trying to solve is as follows: $$ C_m = \frac{{abs{x}}e^{2x}}{\pi^{1/2}}\int_0^t t^{-3/2}e^{-x^2/t-t}dt $$ [image: enter image description here] The code that I am using is as follows: a <- seq(from=-10, by=0.5,length=100) ## Create a function to compute integrationCfun <- function(XX, upper){ integrand <- function(x)x^(-0.5)*exp((-XX^2/x)-x) integrated <-...

Greetings, Sorry, the last message was sent by mistake! Here it is again: I encounter a strange problem computing some numerical integrals on [0,oo). Define $$ M_j(x)=exp(-jax) $$ where $a=0.08$. We want to compute the $L^2([0,\infty))$-inner products $$ A_{ij}:=(M_i,M_j)=\int_0^\infty M_i(x)M_j(x)dx $$ Analytically we have $$ A_{ij}=1/(a(i+j)). $$ In the code below we compute the matrix $A_{i,j}$, $1\leq i,j\leq 5$, numerically and check against the known analytic values. When I run this code most components of A are correct, but some are zero. I get the following output...

Interesting. I gave this a try, but couldn't make this work. One would have to infuse something like <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax at 3/es5/tex-mml-chtml.js"> </script> or <script id="MathJax-script" async src="<url-to-your-site>/mathjax/tex-chtml.js"> </script> into

Greetings,   I encounter a strange problem computing some numerical integrals on [0,oo). Define $$ M_j(x)=exp(-jax) $$ where $a=0.08$. We want to compute the $L^2([0,\infty))$-inner products $$ A_{ij}:=(M_i,M_j)=\int_0^\infty M_i(x)M_j(x)dx $$ Analytically we have $$ A_{ij}=1/(a(i+j)). $$ In the code below we compute the matrix $A_{i,j}$, $1\leq i,j\leq 5$, numerically and check against the known analytic values.   When I run this code most components of A are correct, but some are zero. I get the following outpu...

Dear Prof. Brostr?m, Dear R-mailinglist, first of all thanks a lot for your great effort to incorporate time-varying covariates into aftreg. It works like a charm so far and I'll update you with detailled benchmarks as soon as I have them. I have one more questions regarding Accelerated Failure Time models (with aftreg): You mention that left truncation in combination with time-varying

In 'Writing R Extensions' section 6.9 there is the paragraph There are interfaces (defined in header R_ext/Applic.h) for definite and for indefinite integrals. ?Indefinite? means that at least one of the integration boundaries is not finite. An indefinite integral usually means an antiderivative, not an integral over an infinite spread. Should that first sentence end with 'for

...ration - Gauss Quadrature To: r-help at stat.math.ethz.ch Message-ID: <gbrek1$64m$1 at ger.gmane.org> "Susanne Pfeifer" <tiffy at tiffy.it> wrote in message news:48DE3BE0.5020200 at tiffy.it... > Hi, > > I would like to solve a double integral of the form > > \int_0^1 \int_0^1 x*y dx dy > > using Gauss Quadrature. OK, I felt guilty for using a for loop, so here's something that should be close to what you want using sapply: library(statmod) N <- 5 GL <- gauss.quad(N) nodes <- GL$nodes weights <- GL$weights gauss_legendre2D <- fun...