The probability density function associated with a random variable Z is inverse-invariant if it is identical to the density function associated with the inverse of Z. An intuitive method of finding inverse-invariant density functions is presented, with examples and notes on where these distributions arise. Specific parameter estimation algorithms which produce estimates having inverse-invariant distributions are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>