- #1
TheBoro76
- 7
- 0
Hi, this isn't exactly a homework question, but this seemed like the most appropriate place to put it.
I have an equation in the form:
log(a)=log(b)+c.
I also have standard errors (SEMs) for b and c. I want to find the standard error for log(a) (i.e. log(a) +/- E(log(a)))
I know the SEM of some quantity x, where x:=y+z, is given by Ex=sqrt(Ey^2+Ez^2)
The problem is really trying to find the error of the log.
In high school I would have solved it by choseing the largest of:
abs(log(b+Eb)-log(b)) and abs(log(b-Eb)-log(b)), where Eb is the SEM of b.
if we let this be g then
E(log(a))=sqrt(g^2+Ec^2)
However, given I am doing uni research I am not sure whether this would be acceptable.
I have also considered making a Monte-Carlo simulation of the problem. Drawing random numbers from the distributions b~N(b,Eb) and c~N(c,Ec) and finding the mean and standard deviation of the simulation. However I would like to get an analytical solution.Thanks in advance if anyone can help me out
Homework Statement
I have an equation in the form:
log(a)=log(b)+c.
I also have standard errors (SEMs) for b and c. I want to find the standard error for log(a) (i.e. log(a) +/- E(log(a)))
Homework Equations
I know the SEM of some quantity x, where x:=y+z, is given by Ex=sqrt(Ey^2+Ez^2)
The Attempt at a Solution
The problem is really trying to find the error of the log.
In high school I would have solved it by choseing the largest of:
abs(log(b+Eb)-log(b)) and abs(log(b-Eb)-log(b)), where Eb is the SEM of b.
if we let this be g then
E(log(a))=sqrt(g^2+Ec^2)
However, given I am doing uni research I am not sure whether this would be acceptable.
I have also considered making a Monte-Carlo simulation of the problem. Drawing random numbers from the distributions b~N(b,Eb) and c~N(c,Ec) and finding the mean and standard deviation of the simulation. However I would like to get an analytical solution.Thanks in advance if anyone can help me out