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Assume there are ten data with values $a_1$, $a_2$, ..., $a_{10}$ each with different non-symmetric errors. The problem confronting me in brief is, to combine the 10 results $a_{i}$ and their associated non-symmetric errors according to some acceptable precept so as to determine the value of $a$ and its errors which best represents the aggregate of observations.

I would appreciate any insight into this problem.

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  • $\begingroup$ Could you indicate how these errors were obtained and what exactly you mean by "non-symmetric"? $\endgroup$
    – whuber ♦
    Commented Oct 28, 2017 at 17:24
  • $\begingroup$ Thanks @whuber for your comment. The errors are obtained from a complex modelling code, but suffice to say that the errors come from probability distributions that cannot be characterised with an analytical model (e.g. by a normal distribution, Poisson, etc.). By 'non-symmetric' I mean non-Gaussian. In other words, the positive error is a number which is generally different than the negative error. $\endgroup$
    – user4437416
    Commented Oct 28, 2017 at 17:46
  • $\begingroup$ May we understand, then, that (a) you have an estimate of (or assumption about) each error distribution and (b) all results are independent estimates of an unknown constant $a$? $\endgroup$
    – whuber ♦
    Commented Oct 28, 2017 at 17:47
  • $\begingroup$ Thank you @whuber. To answer (a), I can say the following. The values $a_i$ are the median values of the probability distributions. The positive and negative errors for each datum are gotten from their respective probability distributions considering 34.15 percent of solutions to either side of the median value. And for (b), yes. $\endgroup$
    – user4437416
    Commented Oct 28, 2017 at 17:52

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