Hi.
Should've posted this long ago but I guess it's
better late than never.
Cor Stolk and David Jones pointed out that Ted
Harding's proof (see 1st summary) had implicitly
assumed that the functions were not only
differentiable but also monotonic. See below:
>>>>Ted Harding:
Now suppose x = g(y), and let dx corrspond to dy, so
that dP, the probability that X is in dx, is also the
probability that Y is in dy. <== assumption of
monotonicity.
In this case, Cor proposes a proof which does not rely
on differentiability but only on monotonicity. Also
below proposals for constructing the desired non-linear
functions from Cor, David Jones and David McNulty.
>>>>Cor Stolk:
==> Assume the function is monotonic.
my way of attacking the problem is to look at the
cumulative distribution
function.
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