Hello
after reading few nodes from the info docs. I am not
sure if this task can be done using R:
the density function f(x,y) = 12xy(1-y) for
0<x<1, 0<y<1
the condition of inequality (x-y)> (1/2)
what if the limits of integration are functions of the
variable I am integrating over.
is this somthing which can be done in a simple way,
with R?
examples:
Mathimatic 5.1:
In[2]:=Integrate[12*x*y*(1-y)*Boole[x-y>1/2],{y,0,1},{x,0,1}]
Maple:
Doubleint(12*x*y*(1-y)*Heaviside(x-y-1/2),x=0..1,y=0..1);
many thanks
integration
2 messages · Fred J., Brian Ripley
Numerical integration: yes. Symbolic integration: no.
On Mon, 22 Aug 2005, Fred J. wrote:
after reading few nodes from the info docs. I am not
sure if this task can be done using R:
the density function f(x,y) = 12xy(1-y) for
0<x<1, 0<y<1
the condition of inequality (x-y)> (1/2)
what if the limits of integration are functions of the
variable I am integrating over.
is this somthing which can be done in a simple way,
with R?
examples:
Mathimatic 5.1:
In[2]:=Integrate[12*x*y*(1-y)*Boole[x-y>1/2],{y,0,1},{x,0,1}]
Maple:
Doubleint(12*x*y*(1-y)*Heaviside(x-y-1/2),x=0..1,y=0..1);
Symbolic integration: no.
Numerical integration: yes, e.g.
library(adapt)
adapt(2, c(0,0), c(1,1),
functn=function(x) {y=x[2]; x=x[1]; 12*x*y*(1-y)*(x-y>1/2)})
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595