R help - Jan 2011 - How to compute the density of a variable that follows a proportional error distribution

Hello,
I am trying to compute the density of a variable k that is either (1)
Normally distributed; (2) Log-Normally distributed; or (3) follows
proportional error distribution. I tried to search R-help and the answer for
normal distribution was easy to find (please see 1c). I am not sure if my
formula for dlnorm is correct (please see 2c below)? I really don't know
what function to use for the density of k with a proportional error
distribution.

Please help,
Mahesh


1.       Normal distribution:

*a)   *k=qk+h, hÎN(0, w)

*b)   *then kÎN(qk, w)

*c)    *density of a variable k: dnorm(x,mean=qk,sd=w,log=FALSE) #x: vector
of quantiles



2.       Log-Normal distribution:

*a)   *k=qk exp(h), hÎN(0, w)

*b)   *then kÎLN(qk, w)

*c)    *density of a variable k: dlnorm(x,meanlog=log(qk),sdlog=w,log=FALSE)
*# Is sdlog correct?????*

**

3.       Proportional Error distribution

*a)   *k=qk (1+h), hÎN(0, w)

*???? *

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Hello,
Please accept my apologies; the symbols from my earlier message did not make
it through correctly on the mailing list. Here is my question again:
I am trying to compute the density of a variable k that is either (1)
Normally distributed; (2) Log-Normally distributed; or (3) follows
proportional error distribution. I tried to search R-help and the answer for
normal distribution was easy to find (please see Bullet a below). I am not
sure if my formula for sdlog is correct for dlnorm (please bullet b below)?
I really don't know what function to use for the density of k with a
proportional error distribution (please bullet c).

Please help…Mahesh

a) Normal distribution:
   k = theta+eta, k is a random variable; eta is normally distributed with
mean 0 & sd of omega while theta is a constant
   Density of k is given by: dnorm(x, mean = theta, sd = omega, log = FALSE)
#x is vector of quantiles

b) Log-Normal distribution:
   k= theta*exp(eta), k is a random variable; eta is normally distributed
with mean 0 & sd of omega while theta is a constant
   Density of k is given by: dlnorm(x, meanlog = log(theta), sdlog = omega,
log = FALSE)  #### Is sdlog correct???

c) Proportional Error distribution
   k=theta*(1+eta), k is a random variable; eta is normally distributed with
mean 0 & sd of omega while theta is a constant
   Density of k is given by: ???

I am aware of the density function in R, but is it possible to define of
density of k with a proportional error distribution in terms of theta and
omega?

On Sun, Jan 2, 2011 at 10:08 AM, mahesh samtani <msamtani@gmail.com>
wrote:
> Hello,
> I am trying to compute the density of a variable k that is either (1)
> Normally distributed; (2) Log-Normally distributed; or (3) follows
> proportional error distribution. I tried to search R-help and the answer
for
> normal distribution was easy to find (please see 1c). I am not sure if my
> formula for dlnorm is correct (please see 2c below)? I really don't
know
> what function to use for the density of k with a proportional error
> distribution.
>
> Please help,
> Mahesh
>
>
> 1.       Normal distribution:
>
> *a)   *k=qk+h, hÎN(0, w)
>
> *b)   *then kÎN(qk, w)
>
> *c)    *density of a variable k: dnorm(x,mean=qk,sd=w,log=FALSE) #x:
> vector of quantiles
>
>
>
> 2.       Log-Normal distribution:
>
> *a)   *k=qk exp(h), hÎN(0, w)
>
> *b)   *then kÎLN(qk, w)
>
> *c)    *density of a variable k:
dlnorm(x,meanlog=log(qk),sdlog=w,log=FALSE)
> *# Is sdlog correct?????*
>
> **
>
> 3.       Proportional Error distribution
>
> *a)   *k=qk (1+h), hÎN(0, w)
>
> *???? *
>
>
>
>
>
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