Discrimination between the lognormal and Weibull distributions by using multiple linear regression
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| Format: | Artículo científico |
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Universidad Nacional de Colombia
2018
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| _version_ | 1876432359707901952 |
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| author | Jesús Francisco Ortiz Yañez |
| author_facet | Jesús Francisco Ortiz Yañez |
| contents | Discrimination between the lognormal and Weibull distributions by using multiple linear regression Jesús Francisco Ortiz Yañez Manuel Román Piña Monarrez Ingeniería Gumbel distribution Weibull distribution lognormal distribution discrimination process 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 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. 2018 artículo científico 0012-7353 https://www.redalyc.org/articulo.oa?id=49657889001 https://www.redalyc.org/journal/496/49657889001/ https://www.redalyc.org/journal/496/49657889001/html/ https://www.redalyc.org/journal/496/49657889001/49657889001.epub https://www.redalyc.org/journal/496/49657889001/movil 10.15446/dyna.v85n205.66658 en http://www.redalyc.org/revista.oa?id=496 Dyna application/pdf Universidad Nacional de Colombia Dyna (Colombia) Num.205 Vol.85 |
| format | Artículo científico |
| id | redalyc_49657889001 |
| institution | Redalyc |
| language | en |
| publishDate | 2018 |
| publisher | Universidad Nacional de Colombia |
| spellingShingle | Discrimination between the lognormal and Weibull distributions by using multiple linear regression Jesús Francisco Ortiz Yañez Ingeniería Gumbel distribution Weibull distribution lognormal distribution discrimination process multiple linear regression Discrimination between the lognormal and Weibull distributions by using multiple linear regression Jesús Francisco Ortiz Yañez Manuel Román Piña Monarrez Ingeniería Gumbel distribution Weibull distribution lognormal distribution discrimination process 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 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. 2018 artículo científico 0012-7353 https://www.redalyc.org/articulo.oa?id=49657889001 https://www.redalyc.org/journal/496/49657889001/ https://www.redalyc.org/journal/496/49657889001/html/ https://www.redalyc.org/journal/496/49657889001/49657889001.epub https://www.redalyc.org/journal/496/49657889001/movil 10.15446/dyna.v85n205.66658 en http://www.redalyc.org/revista.oa?id=496 Dyna application/pdf Universidad Nacional de Colombia Dyna (Colombia) Num.205 Vol.85 |
| title | Discrimination between the lognormal and Weibull distributions by using multiple linear regression |
| topic | Ingeniería Gumbel distribution Weibull distribution lognormal distribution discrimination process multiple linear regression |
| url | https://www.redalyc.org/articulo.oa?id=49657889001 https://www.redalyc.org/journal/496/49657889001/ https://www.redalyc.org/journal/496/49657889001/html/ https://www.redalyc.org/journal/496/49657889001/49657889001.epub https://www.redalyc.org/journal/496/49657889001/movil |