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

Amadou Sawadogo et al.

Mathematical Methods of Statistics2025https://doi.org/10.3103/s1066530724600015article
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What the paper says

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 $$\beta$$ is greater, equal and less than the determined value $$\beta_{1}\in(0,1/2)$$ , respectively. Similar result holds for the Weibull distribution with $$\beta_{1}=1$$ and extends the one of two-parameter model. The Newton–Raphson method is used to determine the approximative value $$\beta_{1}=0.37100965$$ of the log-logistic model; it can thus lead to the reference shifted-exponential model, as for $$\beta_{1}=1$$ of the Weibull one. The relative variation between Weibull and log-logistic is also mentioned. Finally, two illustrative applications are provided.

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https://doi.org/https://doi.org/10.3103/s1066530724600015

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@article{amadou2025,
  title        = {{The Shifted-Exponential Variation Property for the Weibull and Log-Logistic Models}},
  author       = {Amadou Sawadogo et al.},
  journal      = {Mathematical Methods of Statistics},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.3103/s1066530724600015},
}

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