R help - Jan 2012 - Solving Equations

People,

I'm researching some Bayesian statistic topics and in the midle of my study
i found a very simple problem and i'm trying to find a simple package to
solve this type of equations:

Lets say that i need to compute beta values for the beta distribution and i
now for example:

E(teta)=a/(a+b) = 0,5
Var(teta)=ab/((a+b)^2(a+b+1))=0.05

So if i want to solve this to non-linear system to find a,b for the beta
distribution wich pack should i use?

I know that a=2 and b=2 because i calculated it. 

Can someone help?

Thanks,
Eliano

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On Jan 22, 2012, at 1:25 PM, Eliano wrote:
> People,
>
> I'm researching some Bayesian statistic topics and in the midle of  
> my study
> i found a very simple problem and i'm trying to find a simple  
> package to
> solve this type of equations:
>
> Lets say that i need to compute beta values for the beta  
> distribution and i
> now for example:
>
> E(teta)=a/(a+b) = 0,5
> Var(teta)=ab/((a+b)^2(a+b+1))=0.05
>
> So if i want to solve this to non-linear system to find a,b for the  
> beta
> distribution wich pack should i use?
>
> I know that a=2 and b=2 because i calculated it.
It depends on you meaning for the word "solve". If you want symbolic  
math, then the Ryacas package provides that facilities. If you want  
numerical estimation, then you should provide the data in your posting  
AND study the help pages for `nls` AND do searches in the Task Views  
AND the rhelp Archives for the wealth of worked examples available .

-- 

David Winsemius, MD
West Hartford, CT

On 22-01-2012, at 19:25, Eliano wrote:
> People,
> 
> I'm researching some Bayesian statistic topics and in the midle of my
study
> i found a very simple problem and i'm trying to find a simple package
to
> solve this type of equations:
> 
> Lets say that i need to compute beta values for the beta distribution and i
> now for example:
> 
> E(teta)=a/(a+b) = 0,5
> Var(teta)=ab/((a+b)^2(a+b+1))=0.05
> 
> So if i want to solve this to non-linear system to find a,b for the beta
> distribution wich pack should i use?
> 
> I know that a=2 and b=2 because i calculated it. 
> 
There is a package nleqslv which can handle you system.


library(nleqslv)

eqf <- function(x) {
    a <- x[1]
    b <- x[2]
    y <- numeric(2)   
    y[1] <- a/(a+b) - 0.5
    y[2] <- a*b/((a+b)^2 * (a+b+1)) -0.05
    y
}
       
x.start <- c(1,1)

nleqslv(x.start,eqf)


Berend

On Sun, Jan 22, 2012 at 1:25 PM, Eliano <eliano.m.marques at gmail.com>
wrote:
> People,
>
> I'm researching some Bayesian statistic topics and in the midle of my
study
> i found a very simple problem and i'm trying to find a simple package
to
> solve this type of equations:
>
> Lets say that i need to compute beta values for the beta distribution and i
> now for example:
>
> E(teta)=a/(a+b) = 0,5
> Var(teta)=ab/((a+b)^2(a+b+1))=0.05
>
> So if i want to solve this to non-linear system to find a,b for the beta
> distribution wich pack should i use?
>
The equations giving a and b as a function of m and v are:
> library(Ryacas)
> a <- Sym("a"); b <- Sym("b")
> m <- Sym("m"); v <- Sym("v")
> Solve( List(a/(a+b) == m, a*b/((a+b)^2*(a+b+1)) == v), List(a, b) )
expression(list(list(a == m^2 * (1 - m)/v - m, b == a/m - a)))

Based on the above we write this R function:

beta.parms <- function(m, v) {
   a <- m^2 * (1-m)/v - m
   b <- a/m - a
   c(a = a, b = b)
}

and run it:
> beta.parms(m = 0.5, v = 0.05)
a b
2 2

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Like the t-shirt says,  "There's no place like 127.0.0.1 "



<quote>
Though I wasn't familiar with this I check the repositories list and 
CRAN (extras) is selected in my installation (R-2.14.1). By the way, 
when trying Ryacas after what seemed to be a successful install, for a 
simple example of

x <- 2
Eval(yacas(expression(x*x)))

I got the following:

[1] "Starting Yacas!"
Error in socketConnection(host = "127.0.0.1", port = 9734, server = 
FALSE, :
    cannot open the connection
In addition: Warning message:
In socketConnection(host = "127.0.0.1", port = 9734, server = FALSE, :

    127.0.0.1:9734 cannot be opened

I tried adding yacas to my firewall exceptions but no help.

David
-- 

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