## The uniform distribution is complete
with respect to testing identity to a fixed distribution

#### Webpage for a paper by Oded Goldreich

#### Abstract

Inspired by Diakonikolas and Kane (2016),
we reduce the class of problems consisting
of testing whenther an unknown distribution over $[n]$
equals a fixed distribution to this very problem
when the fixed distribution is uniform over $[n]$.
Our reduction preserves the parameters of the problem,
which are $n$ and the proximity parameter $\e>0$,
up to a constant factor.
While this reduction yields no new bounds on the
sample complexity of either problems,
it provides a simple way of obtaining testers for equality to arbitrary
fixed distributions from testers for the uniform distribution.

#### Material available on-line

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