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

Jesus Francisco Ortiz-Yañez; Manuel Román Piña Monarrez

Publicado

2018-04-01

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

Discriminación entre la distribución lognormal y la distribución Weibull utilizando regresión lineal múltiple

Palabras clave:

Weibull distribution, lognormal distribution, discrimination process, multiple linear regression, Gumbel distribution (en)
distribución Weibull, distribución lognormal, proceso de discriminación, regresión lineal múltiple, distribución Gumbel (es)

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Autores/as

Jesus Francisco Ortiz-Yañez Universidad Autónoma de Ciudad Juárez https://orcid.org/0000-0002-4807-432X
Manuel Román Piña Monarrez Universidad Autónoma de Ciudad Juárez https://orcid.org/0000-0002-2243-3400

Resumen (en)
Resumen (es)

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 (b_1ln) and Weibull (b_1w) regression coefficients (slopes) b_1ln/b_1w efficiently represents the skew behavior. Thus, since the ratio of the lognormal (R_ln) and Weibull (R_w) correlation coefficients R_ln/R_w (for a fixed sample size) depends only on the b_1ln/b_1w 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.

En el análisis de confiabilidad, las distribuciones Weibull y lognormal son ambas analizadas utilizando el logaritmo de los datos observados. Debido a que mientras el logaritmo de datos Weibull presenta sesgo, el logaritmo de datos lognormales es simétrico, entonces en este artículo basados en 1) los coeficientes de variación (CV), 2) en la desviación estándar del logaritmo de los datos, 3) en la posición del percentil de la media del logaritmo de los datos y 4) en dispersión acumulada del logaritmo antes y después de la media, un método para discriminar entre ambas distribuciones es presentado. La eficiencia del método propuesto está basado en el hecho de que el radio entre los coeficientes de regresión (pendientes) b_1ln/b_1w de la distribución lognormal (b_1ln) y de la distribución Weibull (b_1w), eficientemente representa el comportamiento del sesgo. De esta manera, dado que el radio de los coeficientes de correlación de la distribución lognormal (R_ln) y de la distribución Weibull (R_w), (para un tamaño de muestra fijo), solo depende del radio b_1ln/b_1w, entonces el coeficiente de correlación múltiple R² es utilizado como un índice para discriminar entre ambas distribuciones. Una aplicación y el impacto que una mala selección tiene sobre R(t) son también dadas.

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