# May minimised making any one the and the rest zero

Compression for pdfs

This still has to have integral 1 over the interval which is half the size. The total saving then comes out to be

nats. So we have lost, for every point, one bit on the first

Intuitively, one would expect that there would always *be* a
saving, that the worst case is when the function *f* is constant
when the saving is clearly zero. In other words, reflecting on the
function *f* as distorting the density of points in the space and
on coding this information suitably as a way of expressing the data more
efficiently, leads

one to the belief that will be non-negative for any
function *f* such that

it is easy to see that the expression is maximised when

http://ciips.ee.uwa.edu.au/~mike/PatRec/node84.html (5 of 8) [12/12/2000 4:15:15 AM]

lies between
-*log*(*M*) and 0:

which becomes

The zero value is attained only for the uniform distribution.

The cheerful, and some would say irresponsible, treatment of limits will give a severe case of the uglies to