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Science Forum Index » Space - Consult Forum » calculating confidence interval for a sum of forecasts...
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| mehtakrishna2002 at (no spam) yahoo.com... |
 Posted: Mon Jun 23, 2008 11:08 am |
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Guest
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Hi,
I am generating forecasts for 10 clusters and have the 95% confidence
interval for each of them. I am now trying to calculate the
confidence intervals for the sum of the forecasts for the 10 clusters.
I would appreciate it if somebody could point me to the correct
formula?
Thanks for your help.
K |
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| Aniko... |
| Posted: Mon Jun 23, 2008 12:08 pm |
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Guest
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On Jun 23, 4:08 pm, "mehtakrishna2... at (no spam) yahoo.com"
<mehtakrishna2... at (no spam) yahoo.com> wrote:
Quote: Hi,
I am generating forecasts for 10 clusters and have the 95% confidence
interval for each of them. I am now trying to calculate the
confidence intervals for the sum of the forecasts for the 10 clusters.
I would appreciate it if somebody could point me to the correct
formula?
Thanks for your help.
K
Are the forecasts independent? How did you get the individual
confidence intervals (eg. from a normal distribution)?
Aniko |
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| Aniko... |
| Posted: Wed Jun 25, 2008 3:24 am |
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Guest
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On Jun 23, 5:08 pm, Aniko <aniko123... at (no spam) yahoo.com> wrote:
Quote: On Jun 23, 4:08 pm, "mehtakrishna2... at (no spam) yahoo.com"
mehtakrishna2... at (no spam) yahoo.com> wrote:
Hi,
I am generating forecasts for 10 clusters and have the 95% confidence
interval for each of them. I am now trying to calculate the
confidence intervals for the sum of the forecasts for the 10 clusters.
I would appreciate it if somebody could point me to the correct
formula?
Thanks for your help.
K
Are the forecasts independent? How did you get the individual
confidence intervals (eg. from a normal distribution)?
Aniko
Since in a private e-mail you told me that the forecast are indeed
independent, and normally distributed, this becomes a simple problem.
If Xi ~ N(mi, si^2) is the measurement for the i-th cluster, then
X=sum(Xi) ~ N(sum(mi), sum(si^2)) as long as they are independent. So
you can construct a confidence interval for sum(mi) the same way as
you did for mi, but using sqrt(sum(si^2)) for the new standard
deviation.
Aniko |
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| Posted: Wed Jun 25, 2008 8:01 am |
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Guest
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I have a somewhat similar problem, where I am using a linear model to
describe leaching of a chemical as a function of rainfall amount. I
would like to calculate 95% prediction intervals for the cumulative
leaching from the beginning of the simulation to after *each* of n
rainfalls (including all the rainfalls up to and including the ith
rainfall). Leaching was log-transformed, so I will have to
exponentiate the predictions before adding them. I've assumed I would
have to do this with a Monte Carlo simulation, but is there another
way? |
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