Analysis of extreme rainfall using the log logistic distribution

Fitzgerald, D. L.

doi:10.1007/s00477-004-0229-x

Cited by 13 publications

(4 citation statements)

References 8 publications

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“…In experiment C1, the GLO, a model that originates in hydrology (Ahmad et al 1988) and may be a suitable alternative also for maxima of daily precipitation amounts (Fitzgerald 2005;Kyselý and Picek 2007), is used as parent, but a GEV distribution is utilized for the estimation. Again, the parameterization of Hosking and Wallis (1997) for the GLO distribution is used, that is, a reparameterized version of the log-logistic distribution of Ahmad et al (1988), in which the parameters are analogous to those of the GEV distribution.…”

Section: Experiments A3a and A3b (The Gumbel Distribution As Parent)mentioning

confidence: 99%

A Cautionary Note on the Use of Nonparametric Bootstrap for Estimating Uncertainties in Extreme-Value Models

Kyselý

2008

Journal of Applied Meteorology and Climatology

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The parametric and nonparametric approaches to the bootstrap are compared as to their performance in estimating uncertainties in extreme-value models. Simulation experiments make use of several combinations of true and fitted probability distributions utilized in climatological and hydrological applications. The results demonstrate that for small to moderate sample sizes the nonparametric bootstrap should be interpreted with caution because it leads to confidence intervals that are too narrow and underestimate the real uncertainties involved in the frequency models. Although the parametric bootstrap yields confidence intervals that are slightly too liberal as well, it improves the uncertainty estimates in most examined cases, even under conditions in which an incorrect parametric model is adopted for the data. Differences among three examined types of bootstrap confidence intervals (percentile, bootstrap t, and bias corrected and accelerated) are usually smaller in comparison with those between the parametric and nonparametric versions of bootstrap. It is concluded that the parametric bootstrap should be preferred whenever inferences are based on small to moderate sample sizes (n Յ 60) and a suitable model for the data is known or can be assumed, including applications to confidence intervals related to extremes in global and regional climate model projections.

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Section: Experiments A3a and A3b (The Gumbel Distribution As Parent)mentioning

confidence: 99%

A Cautionary Note on the Use of Nonparametric Bootstrap for Estimating Uncertainties in Extreme-Value Models

Kyselý

2008

Journal of Applied Meteorology and Climatology

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“…As it has been widely deployed in many research areas, the EVD is used to represent the distributions of various observations. ese include wind speed and energy data [4,[8][9][10][11][12], wave data prediction [13], data on air pollution [14][15][16][17][18], information and communication technology [19], data on flooding [20], financial risk [3,21], temperature [22], food drying technology [23], and rainfall [24]. It has also been implemented in public health and medical sciences [25,26].…”

Section: Introductionmentioning

confidence: 99%

Extreme Value Distributions: An Overview of Estimation and Simulation

Abdulali

Bakar

Ibrahim

et al. 2022

Journal of Probability and Statistics

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The generalized extreme value distribution (GEVD) and various extreme value distributions are commonly applied in air pollution, telecommunications, operational risk management, finance, insurance, material sciences, economics, and hydrology, among many other industries that deal with extreme events. Extreme value distributions (EVDs) typically limit the distribution of maximum and minimum values for many random observations drawn from the same arbitrary distribution. Besides that, it is a crucial method for forecasting future events and emerged as critical method for predicting future events. As a result, prior research is required to select the best estimation method to obtain a reliable value for the parameters of extreme value distributions. This study provides an overview of three-parameter estimation methods based on goodness-of-fit statistics and root mean square error (RMSE). This paper reviewed and compared three estimation methods used to approximate values of parameters for simulated observations taken from the EVD and GEVD. The method of moments (MOMs), maximum likelihood estimator (MLE), and maximum product of spacing (MPS) were the methods investigated in this study. Our findings indicated that the MPS performed better based on the mean square errors (MSEs); meanwhile, the MPS had similar goodness-of-fit statistic values compared to the MLE.

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“…Considering the wet months, the amount of monthly rainfall has positive value and usually the histograms appear to be positively skewed. So, the probability distributions used for this purpose are right-skewed and defined on the positive real line; some examples are exponential (Todorovic and Woolhiser, 1975;Burgueño et al, 2005Burgueño et al, , 2010Hazra et al, 2018), gamma (Barger and Thom, 1949;Mooley and Crutcher, 1968;Husak et al, 2007;Krishnamoorthy and León-Novelo, 2014), log-normal (Kwaku and Duke, 2007;Sharma and Singh, 2010), Weibull (Duan et al, 1995;Burgueño et al, 2005;Lana et al, 2017), Pearson Type-III/V/VI (Hanson and Vogel, 2008;Khudri and Sadia, 2013;Mayooran and Laheetharan, 2014) and log-logistic (Fitzgerald, 2005;Sharda and Das, 2005). Out of several possible choices, the first four are mostly used in meteorological literature and hence we also concentrate only on those four distributions in this paper.…”

Section: Introductionmentioning

confidence: 99%

Robust statistical modeling of monthly rainfall: The minimum density power divergence approach

Hazra¹,

Ghosh²

2019

Preprint

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Statistical modeling of rainfall is an important challenge in meteorology, particularly from the perspective of rainfed agriculture where a proper assessment of the future availability of rainwater is necessary. The probability models mostly used for this purpose are exponential, gamma, Weibull and lognormal distributions, where the unknown model parameters are routinely estimated using the maximum likelihood estimator (MLE). However, presence of outliers or extreme observations is quite common in rainfall data and the MLEs being highly sensitive to them often leads to spurious inference. In this paper, we discuss a robust parameter estimation approach based on the minimum density power divergence estimators (MDPDEs) which provides a class of estimates through a tuning parameter including the MLE as a special case. The underlying tuning parameter controls the trade-offs between efficiency and robustness of the resulting inference; we also discuss a procedure for datadriven optimal selection of this tuning parameter as well as robust selection of an appropriate model that provides best fit to some specific rainfall data. We fit the above four parametric models to the areally-weighted monthly rainfall data from the 36 meteorological subdivisions of India for the years 1951-2014 and compare the fits based on the MLE and the proposed optimum MDPDE; the superior performances of the MDPDE based approach are illustrated for several cases. For all month-subdivision combinations, the best-fit models and the estimated median rainfall amounts are provided. Software (written in R)

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Analysis of extreme rainfall using the log logistic distribution

Cited by 13 publications

References 8 publications

A Cautionary Note on the Use of Nonparametric Bootstrap for Estimating Uncertainties in Extreme-Value Models

A Cautionary Note on the Use of Nonparametric Bootstrap for Estimating Uncertainties in Extreme-Value Models

Extreme Value Distributions: An Overview of Estimation and Simulation

Robust statistical modeling of monthly rainfall: The minimum density power divergence approach

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