The transform arises in applications of Stein's method in probability and statistics.
The zero bias transform of its density function f(t) is a new density function g(s) defined by[1][2] An equivalent but alternative approach is to deduce the nature of the transformed random variable by evaluating the expected value where the right-side superscript denotes a zero biased random variable whereas the left hand side expectation represents the original random variable.
The zero bias transformation arises in applications where a normal approximation is desired.
Similar to Stein's method the zero bias transform is often applied to sums of random variables with each summand having finite variance an mean zero.
This example shows that the zero bias transform takes continuous symmetric distributions and makes them unimodular.