  We present a method for mapping variations between probability distribution
functions and apply this method within the context of measuring galaxy redshift
distributions from imaging survey data. This method, which we name PITPZ for
the probability integral transformations it relies on, uses a difference in
curves between distribution functions in an ensemble as a transformation to
apply to another distribution function, thus transferring the variation in the
ensemble to the latter distribution function. This procedure is broadly
applicable to the problem of uncertainty propagation. In the context of
redshift distributions, for example, the uncertainty contribution due to
certain effects can be studied effectively only in simulations, thus
necessitating a transfer of variation measured in simulations to the redshift
distributions measured from data. We illustrate the use of PITPZ by using the
method to propagate photometric calibration uncertainty to redshift
distributions of the Dark Energy Survey Year 3 weak lensing source galaxies.
For this test case, we find that PITPZ yields a lensing amplitude uncertainty
estimate due to photometric calibration error within 1 per cent of the truth,
compared to as much as a 30 per cent underestimate when using traditional
methods.
