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The Shifted-Exponential Variation Property for the Weibull and Log-Logistic Models

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Pubblicato in:Mathematical Methods of Statistics vol. 34, no. 1 (Mar 2025), p. 67
Autore principale: Sawadogo, Amadou
Altri autori: Bourguignon, Marcelo, Kokonendji, Célestin C.
Pubblicazione:
Springer Nature B.V.
Soggetti:
Newton-Raphson method
Weibull distribution
Datasets
Random variables
Confidence intervals
Parameters
Demography
Maximum likelihood method
Mathematical models
Statistical analysis
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Abstract: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.
ISSN:1066-5307
1934-8045
DOI:10.3103/S1066530724600015
Fonte:ABI/INFORM Global