Fitting continuous probability density functions over [0,infty) using information theory ideas (Corresp.)

The problem of estimating a probability density function
p(x)
over
[0, \infty)
when several low-order moments are known is considered. A computational procedure, based on information theory, is used to obtain the maximum entropy estimates of
p(x)
in a number of cases. The situation when the first two moments only are known is considered in some detail. A table is included for estimating
p(x)
when given
\mu_1 ^{\prime} , \mu_2 ^{\prime}
with
\mu_2 ^{\prime} \leq 2(\mu_1 ^{\prime}) ^ 2
.