ABSTRACT
In opposition to the originally proposed Log‐logistic distribution, Stagge et al. (2015) recommended the use of the general extreme value (GEV) distribution to calculate the standardized ...precipitation evapotranspiration index (SPEI). This is not an irrelevant issue, as the use of different distribution functions may lead to different SPEI values, and thus can make them not compatible with those of other users. Stagge et al. (2015) based their recommendation on the results of goodness‐of‐fit tests applied to climate data in Europe. Here we provide evidence that these tests do not have enough power for discriminating between very similar distribution functions. Even more, their results are not robust and depend on the data used. Other criteria based on the adaptation to the tails of the distribution and the fraction of cases with no solution are more relevant to guide the selection of the most adequate distribution. We have tested both distribution functions based on these criteria and using global gridded data of precipitation and reference evapotranspiration. Our results clearly recommend the use of the Log‐logistic distribution to calculate the SPEI, as originally proposed by Vicente‐Serrano et al. (2010a).
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
ABSTRACT
This response expands on the analysis performed in ‘Candidate Distributions for Climatological Drought Indices (SPI and SPEI)’ by explaining several topics in greater detail and by testing ...the conclusions of our original article against the claims made in the comment by Drs Vicente‐Serrano and Begueria. Tests using the same 11 climate time series confirm the original findings from Stagge et al. (2015) that the Generalized Extreme Value (GEV) distribution produces consistently better fits. Claims that the GEV distribution exaggerates extreme SPEI values were found to be false by comparing Log‐Logistic and GEV‐generated SPEI values directly to the baseline normal distribution, rather than to one another. Once compared with the theoretical normal distribution, the GEV distribution was shown to better model the extreme tails, while the Log‐Logistic distribution consistently underestimated these values. Analysis of the tails was shown to introduce significant uncertainty due to extrapolation regardless of the distribution. We thus strongly disagree with claims made in the comment by Vicente‐Serrano and Begueria that their results clearly recommend the Log‐Logistic distribution. Instead, we prove that differences tend to be small, but consistently support the use of the GEV distribution for SPEI analysis across multiple data sources and goodness of fit metrics.
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The Evaporative Demand Drought Index (EDDI), based on atmospheric evaporative demand, was proposed by Hobbins et al. (2016) to analyse and monitor drought. The EDDI uses a nonparametric approach in ...which empirically derived probabilities are converted to standardized values. This study evaluates the suitability of eight probability distributions to compute the EDDI at 1‐, 3‐ and 12‐month time scales, in order to provide more robust calculations. The results showed that the Log‐logistic distribution is the best option for generating standardized values over very different climate conditions. Likewise, we contrasted this new parametric methodology to compute EDDI with the original nonparametric formulation. Our findings demonstrate the advantages of adopting a robust parametric approach based on the Log‐logistic distribution for drought analysis, as opposed to the original nonparametric approach. The method proposed in this study enables effective implementation of EDDI in the characterization and monitoring of droughts.
This study evaluates the suitability of eight probability distributions to compute the Evaporative Demand Drought Index (EDDI) at 1‐, 3‐ and 12‐month time scales. The results showed that the Log‐logistic distribution is the best option for generating standardized values over very different climate conditions. For this reason, we recommended a robust parametric methodology to compute the EDDI based on the Log‐logistic distribution as opposed to the original nonparametric approach. The method proposed in this study enables effective implementation of EDDI in the analysis and monitoring of droughts.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
We consider log-growth rates of Romanian cities’ populations for all cities in the country in the period 1992-2019 on an annual basis. We construct annual, quinquennial and decennial log-growth rates ...and fit to them thirty-one different statistical distributions. The best results with Kolmogorov–Smirnov, Cramér–von Mises and Anderson–Darling statistics are obtained by a mixture of five stretched Gaussian distributions (5sG) with some fixed parameters, and with the AIC, BIC, HQC information criteria are obtained with mixtures of three logistic distributions (3L), that may have or may have not exponential tails. Just as an illustration, we propose a generating stochastic mechanism for the 3L. Dedicated to Laura Andrés Alcalde
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•We propose a general unit hydrography (GUH) distribution for wind speed statistics.•The GUH distribution is a generalized logistic distribution with a closed form.•The GUH model removes the ...limitation of a zero initial condition in the Weibull model.
We here introduce a simple, general, and analytical method based on the general unit hydrograph (GUH) theory proposed by Guo (2022a, 2022b, 2022c) to describe wind speed marginal distribution. Wind speed probability is generally described by the Weibull distribution; however, its accuracy depends on the contribution made by null wind speed (owing to its zero initial condition). To overcome this disadvantage, we propose a three-parameter GUH distribution with significant flexibility in modeling symmetric heavy-tailed distributions as well as skewed distributions. We show that our proposed GUH distribution corresponds to a generalized logistic distribution that contains both type I and type II generalized logistic distributions. The shape properties of the GUH distribution are discussed along with a simple method for estimating parameters by means of least squares methods. The flexibility of the proposed GUH distribution was assessed by applying it to a well reconstructed global gridded wind speed dataset. Subsequently, we quantify the changes caused by a reversal in global surface wind speed stilling using our GUH distribution. Finally, we confirm that our proposed GUH model agrees with reconstructed wind speed data better than conventional Weibull distribution models, which suggests that the new distribution can be a useful tool for sustainable development of wind energy.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
With the large ongoing number of aged people and Alzheimer's disease (AD) patients worldwide, unpaid caregivers have become the primary sources of their daily caregiving. Alzheimer's family ...caregivers often suffer from physical and mental morbidities owing to various reasons. The aims of this paper were to develop alternate methods to understand the transition properties, the dynamic change, and the long‐run behavior of AD caregivers' stress levels, by assuming their transition to the next level only depends on the duration of the current stress level. In this paper, we modeled the transition rates in the semi‐Markov Process with log‐logistic hazard functions. We assumed the transition rates were non‐monotonic over time and the scale of transition rates depended on covariates. We also extended the uniform accelerated expansion to calculate the long‐run probability distribution of stress levels while adjusting for multiple covariates. The proposed methods were evaluated through an empirical study. The application results showed that all the transition rates of caregivers' stress levels were right skewed. Care recipients' baseline age was significantly associated with the transitions. The long‐run probability of severe state was slightly higher, implying a prolonged recovery time for severe stress patients.
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In many industries, the reliability of a product is often determined by a quantile of a distribution of a product's characteristics meeting a specified requirement. A typical approach to address this ...is to assume a parametric model and compute a one‐sided confidence bound on the quantile. However, this can become difficult if the sample size is too small to reliably estimate such a parametric model. Linear interpolation between order statistics is a viable nonparametric alternative if the sample size is sufficiently large. In most cases, linear extrapolation from the extreme order statistics can be used, but can result in inconsistent coverage. In this work, we perform an empirical study to generate robust weights for linear extrapolation that greatly improves the accuracy of the coverage across a feasible range of distribution families with positive support. Our method is applied to two industrial datasets.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
Oliveira et al. (
2016
) introduced a new continuous model called the McDonald half-logistic (McHL) distribution. They made some mistakes in presenting the log-likelihood function and the score ...functions. In this note, we will correct them.
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A modified version of the three-compartment susceptible-infectious-removed (SIR) epidemic model can be expressed exactly using a specific generalization of the logistic distribution, and its ...parameters can be estimated from epidemic surveillance data. The population proportion remaining Susceptible may be approximated using the inverse of a standard cumulative logistic distribution, while the population proportion actively Infectious may be approximated using the density of a logistic or log-logistic distribution. This knowledge may enable rapid local disease modeling without specialized skills.
Highlights
A modification of the three-compartment SIR model can be solved exactly in terms of a specific generalization of the logistic distribution
The generalized logistic solution can be approximated using standard logistic and/or log-logistic distributions
Surveillance data from an emerging epidemic, often initially modeled with standard logistic or log-logistic curves, can be used to derive parameters for an underlying modified SIR model
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