Discrimination between the lognormal and Weibull Distributions by using multiple linear regression

In reliability analysis, both the Weibull and the lognormal distributions are analyzed by using the observed data logarithms. While the Weibull data logarithm presents skewness, the lognormal data logarithm is symmetrical. This paper presents a method to discriminate between both distributions based...

Full description

Autores:
Ortiz-Yañez, Jesus Francisco
Piña Monarrez, Manuel Román
Tipo de recurso:
Article of journal
Fecha de publicación:
2018
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/68502
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/68502
http://bdigital.unal.edu.co/69535/
Palabra clave:
62 Ingeniería y operaciones afines / Engineering
Weibull distribution
lognormal distribution
discrimination process
multiple linear regression
Gumbel distribution
distribución Weibull
distribución lognormal
proceso de discriminación
regresión lineal múltiple
distribución Gumbel
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
Description
Summary:In reliability analysis, both the Weibull and the lognormal distributions are analyzed by using the observed data logarithms. While the Weibull data logarithm presents skewness, the lognormal data logarithm is symmetrical. This paper presents a method to discriminate between both distributions based on: 1) the coefficients of variation (CV), 2) the standard deviation of the data logarithms, 3) the percentile position of the mean of the data logarithm and 4) the cumulated logarithm dispersion before and after the mean. The efficiency of the proposed method is based on the fact that the ratio of the lognormal (b1ln) and Weibull (b1w) regression coefficients (slopes) b1ln/b1w efficiently represents the skew behavior. Thus, since the ratio of the lognormal (Rln) and Weibull (Rw) correlation coefficients Rln/Rw (for a fixed sample size) depends only on the b1ln/b1w ratio, then the multiple correlation coefficient R2 is used as the index to discriminate between both distributions. An application and the impact that a wrong selection has on R(t) are given also.