Academic Editor: A. Thavaneswaran
Copyright © 2009 Jin Xia et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Lognormal distribution has abundant applications in various fields. In literature,
most inferences on the two parameters of the lognormal distribution are
based on Type-I censored sample data. However, exact measurements are not always
attainable especially when the observation is below or above the detection
limits, and only the numbers of measurements falling into predetermined intervals
can be recorded instead. This is the so-called grouped data. In this paper, we will
show the existence and uniqueness of the maximum likelihood estimators of the two
parameters of the underlying lognormal distribution with Type-I censored data and
grouped data. The proof was first established under the case of normal distribution
and extended to the lognormal distribution through invariance property. The
results are applied to estimate the median and mean of the lognormal population.