Abstract
In this paper we consider the situation where we know the sum of n independent observations from the same probability distribution. We investigate how to empirically determine the marginal probability distributions of the different order statistics conditional upon knowing the sum. This research was motivated by explorations in process improvement where we know the total expected value or variance of a key measure of an n-step process and would like to estimate the proportion of the expected value or variance that is contributed by the most important step (i.e. the single step having the largest expected value or variance), the two most important steps, etc. Both graphical and tabular results are presented for exponential, gamma and normal distributions.
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Silver, E.A., Costa, D. & Zangwill, W. Order statistics of independent identically distributed variables when the sum is known. Statistics and Computing 8, 253–265 (1998). https://doi.org/10.1023/A:1008961428961
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DOI: https://doi.org/10.1023/A:1008961428961