On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

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.

High-performance liquid chromatography measurement of carotenoids in human serum, etoposide in pig cerebrospinal fluid and measurement of the aggregation of xanthophylls in aqueous solutions

The present study measured a chemotherapy drug, etoposide, in pig cerebrospinal fluid after intraventricular administrations were made directly into the fourth ventricle of the brain; cytotoxic concentrations for a twenty-four hour period after infusions. The analytical method developed validates the potential treatment of malignant brain tumors. The increase in serum carotenoid concentration in 30 healthy individuals was measured after supplementation with lutein. HPLC analysis of serum levels of carotenoids showed an increase in the concentration of lutein and a constant concentration of other major serum carotenoids. An initial attempt to measure the enthalpy of aggregation of xanthophylls was conducted by using ultraviolet-visible spectroscopy. The enthalpy of lutein aggregation and AH range of zeaxanthin disordering of aggregation are reported. Monomethyl ether of lutein did not aggregate in any of the aqueous solutions.