Date of this Version
6-16-2009
Document Type
Article
Abstract
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.
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Recommended Citation
Jin Xia, Jie Mi, and YanYan Zhou, “On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data,” Journal of Probability and Statistics, vol. 2009, Article ID 310575, 16 pages, 2009. doi:10.1155/2009/310575
Rights Statement
In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/
This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
Comments
Originally published in Journal of Probability and Statistics.