Lognormal distributions are one of the most commonly studied models in
the sta- tistical literature while being most frequently used in the
applied literature. The lognormal distributions have been used in
problems arising from such diverse fields as hydrology, biology,
communication engineering, environmental science, reliability,
agriculture, medical science, mechanical engineering, material science,
and pharma- cology. Though the lognormal distributions have been around
from the beginning of this century (see Chapter 1), much of the work
concerning inferential methods for the parameters of lognormal
distributions has been done in the recent past. Most of these methods of
inference, particUlarly those based on censored samples, involve
extensive use of numerical methods to solve some nonlinear equations.
Order statistics and their moments have been discussed quite extensively
in the literature for many distributions. It is very well known that the
moments of order statistics can be derived explicitly only in the case
of a few distributions such as exponential, uniform, power function,
Pareto, and logistic. In most other cases in- cluding the lognormal
case, they have to be numerically determined. The moments of order
statistics from a specific lognormal distribution have been tabulated
ear- lier. However, the moments of order statistics from general
lognormal distributions have not been discussed in the statistical
literature until now primarily due to the extreme computational
complexity in their numerical determination.
