The Shifted-Exponential Variation Property for the Weibull and Log-Logistic Models
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| Publicado en: | Mathematical Methods of Statistics vol. 34, no. 1 (Mar 2025), p. 67 |
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Springer Nature B.V.
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| Acceso en línea: | Citation/Abstract Full Text Full Text - PDF |
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| 100 | 1 | |a Sawadogo, Amadou |u UFR de Mathématiques et Informatique, Université Félix Houphouët Boigny, Abidjan, Côte d’Ivoire (GRID:grid.410694.e) (ISNI:0000 0001 2176 6353) | |
| 245 | 1 | |a The Shifted-Exponential Variation Property for the Weibull and Log-Logistic Models | |
| 260 | |b Springer Nature B.V. |c Mar 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a In this paper, the recent shifted-exponential variation property which is defined as the ratio of variance to the squared of shifted expectation is investigated for both three-parameter Weibull and log-logistic models. These nonnegative semicontinuous models are widely considered in engineering, economics, hydrology, demography and many other fields. It is shown that the log-logistic distribution corresponds to over-, equi-, and under-varied if and only if its only positive shape parameter <inline-graphic specific-use="web" mime-subtype="GIF" xlink:href="12004_2025_5066_Article_IEq1.gif" /> is greater, equal and less than the determined value <inline-graphic specific-use="web" mime-subtype="GIF" xlink:href="12004_2025_5066_Article_IEq2.gif" />, respectively. Similar result holds for the Weibull distribution with <inline-graphic specific-use="web" mime-subtype="GIF" xlink:href="12004_2025_5066_Article_IEq3.gif" /> and extends the one of two-parameter model. The Newton–Raphson method is used to determine the approximative value <inline-graphic specific-use="web" mime-subtype="GIF" xlink:href="12004_2025_5066_Article_IEq4.gif" /> of the log-logistic model; it can thus lead to the reference shifted-exponential model, as for <inline-graphic specific-use="web" mime-subtype="GIF" xlink:href="12004_2025_5066_Article_IEq3.gif" /> of the Weibull one. The relative variation between Weibull and log-logistic is also mentioned. Finally, two illustrative applications are provided. | |
| 653 | |a Newton-Raphson method | ||
| 653 | |a Weibull distribution | ||
| 653 | |a Datasets | ||
| 653 | |a Random variables | ||
| 653 | |a Confidence intervals | ||
| 653 | |a Parameters | ||
| 653 | |a Demography | ||
| 653 | |a Maximum likelihood method | ||
| 653 | |a Mathematical models | ||
| 653 | |a Statistical analysis | ||
| 700 | 1 | |a Bourguignon, Marcelo |u Departamento de Estatistica, Universidade Federal do Rio Grande do Norte, Natal, Brazil (GRID:grid.411233.6) (ISNI:0000 0000 9687 399X) | |
| 700 | 1 | |a Kokonendji, Célestin C. |u Laboratoire de Mathématiques de Besançon UMR 6623 CNRS-UMPL, Université Marie & Louis Pasteur, Besançon Cedex, France (GRID:grid.411233.6); Laboratoire de Mathématiques et Connexes de Bangui, Université de Bangui, Bangui B.P., Central African Republic (GRID:grid.25077.37) (ISNI:0000 0000 9737 7808) | |
| 773 | 0 | |t Mathematical Methods of Statistics |g vol. 34, no. 1 (Mar 2025), p. 67 | |
| 786 | 0 | |d ProQuest |t ABI/INFORM Global | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3256938764/abstract/embedded/L8HZQI7Z43R0LA5T?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text |u https://www.proquest.com/docview/3256938764/fulltext/embedded/L8HZQI7Z43R0LA5T?source=fedsrch |
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