In the mixture k ≥ 2 of logarithmic-normal distributions, with density function (1), the parameters μ1, ..., μk satisfying conditions (2) and the parameters p1, ..., pk satisfying conditions (3) are unknown. Using moments of orders r = -k, -k+1, ..., 0, 1, ..., k-1 we get a system of 2k equations (8), an equivalent of matrix equation (10). The equation (13) has exactly one solution with regard to A. If in the equation (13) we substitute the unbiased and consistent estimators D'r for the coefficients Dr, we can get the matrix A with the estimators a'i of the coefficients ai in the equation (11) and the estimators of the roots of the above equations C1 ≤ ... ≤ Ck. Consequently on the basis of (6) we get the estimators μi, i = 1, ..., k. Similarly on the basis of equation (16) and the condition (3) we get the estimators of the remaining parameters. The author does not know any other papers dealing with the estimation of the mixture parameters of finite number of identical distributions where moments of negative order are used.
@article{urn:eudml:doc:40519,
title = {Estimation of the parameters of the mixture k $\geq$ 2 of logarithmic-normal distributions.},
journal = {Trabajos de Estad\'\i stica},
volume = {3},
year = {1988},
pages = {167-175},
zbl = {0731.62075},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40519}
}
Wasilewski, Mariusz J. Estimation of the parameters of the mixture k ≥ 2 of logarithmic-normal distributions.. Trabajos de Estadística, Tome 3 (1988) pp. 167-175. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40519/