Bayesian Estimation of Means and Variances of LogNormal Distributions

_ Lognormal distribution is described by parameters mu and sigma^2, which are parameters of the normal distribution from which the lognormal distribution is derived. Hence, parameters mu and sigma do not correspond simply to the shape of the lognormal distribution. But, if the lognormal distribution is described by its mean and variance, denoted by Mu and Sigma^2, respectively, the parameters Mu and Sigma^2 correspond directly to the location and dispersion of the distribution, respectively. By this parameterization, their interpretation becomes intuitively easy. Using Bayesian analysis, posterior probability of difference between parameters Mus can be gotten. This probability simply represents that of difference. For details, check the file bameans.pdf in the Files box below, in which an example of the analysis is shown. Files used in bemeans.pdf were archived in the file bameansfiles.zip in the Files box below. _

Publication Details

Journal
Open Science Framework
Published
2025-01-01
DOI
https://doi.org/10.17605/osf.io/mgdvy
Primary Topic
Statistical Distribution Estimation and Applications
Type
article
Field-Weighted Citation Impact
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article

Bayesian Estimation of Means and Variances of LogNormal Distributions

Open Science Framework
Statistical Distribution Estimation and Applications
article

Bayesian Estimation of Means and Variances of LogNormal Distributions

article en

Abstract

_ Lognormal distribution is described by parameters mu and sigma^2, which are parameters of the normal distribution from which the lognormal distribution is derived. Hence, parameters mu and sigma do not correspond simply to the shape of the lognormal distribution. But, if the lognormal distribution is described by its mean and variance, denoted by Mu and Sigma^2, respectively, the parameters Mu and Sigma^2 correspond directly to the location and dispersion of the distribution, respectively. By this parameterization, their interpretation becomes intuitively easy. Using Bayesian analysis, posterior probability of difference between parameters Mus can be gotten. This probability simply represents that of difference. For details, check the file bameans.pdf in the Files box below, in which an example of the analysis is shown. Files used in bemeans.pdf were archived in the file bameansfiles.zip in the Files box below. _

Open Science Framework
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Openalex Percentile: Top 48%
Statistical Distribution Estimation and Applications
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