Dear R/Statistics-gurus!

I tried to find answer to my hypothetical question and in vain. Sorry, I
don't have a dataset that fits into this hypothetical question and pardon me
if my explanations/use of statistical terms are not accurate.

It does sound a weird question, but I want to rule out that line of thought.
Is it possible to develop a model (or a simulation) such that the upper
variability is different from lower variability? e.g, the upper variability
in the data above a model predicted value may be less than the variability
in the data below a model predicted value. I guess mixture model is not
applicable here

Around a population estimate (say, mean or maximum likelihood) one of the
following may apply:
total standard deviation (SD) = SD(lower) + SD(upper)
total variance (var) = var(lower) + var(upper);

If it is possible, how do I assign variability in parameters and residual
(additive + proportional) errors?
To fit the observed,
Y = F + (a^2 +b^2/F^2)
F = f(x,Ai, var(Ai)); where Ai = a matrix of parameters; x = a vector
independent variables; var(Ai) = variability in the parameter (Ai)

Regards,
Santosh

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