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I'm summing loan application amounts for a fixed time frame. Is there a way to attach an error on the sum?

I was thinking of assuming some distribution for the amounts and estimating the population spread. And also assuming that an application is some kind of (Poisson?) process, so that the number of applications is also uncertain. Maybe one can multiply both spreads (in amount and number).

Does it make sense and how to actually calculate that?

Gere
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  • Are you looking to compute a confidence interval for average loan application amount? If so, consider bootstrap resampling. – Creosote Dec 16 '15 at 14:16
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    Actually I rather care about the sum. So the number of applications is also a random variable. Or to put it another way: If I collect data for one month and sum up, how can I use this single month to make a guess for the distribution of sums for all following months? – Gere Dec 16 '15 at 18:17
  • Do you have a set of monthly data? Then you can estimate a distribution for the number of summands, and then first simulate from that distribution, then doing bootstrapping from your data that number of times, repeat ... see also https://stats.stackexchange.com/questions/74406/variance-of-sum-of-random-number-of-random-variables-cambridge-university-works – kjetil b halvorsen Jul 26 '23 at 20:56

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