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Here, we investigate the use of rolling-windowed L-moments (RWLMs) and L-moment ratio diagrams (LMRDs) combined with a Multiple Linear Regression (MLR) machine learning algorithm to model non-stationary low-flow hydrological extremes with the potential to simultaneously understand time-variant shape, scale, location, and probability distribution (PD) shifts under climate change. By employing LMRDs, we analyse changes in PDs and their parameters over time, identifying key environmental predictors such as lagged precipitation for September 5-day low-flows. Our findings indicate a significant relationship between total August precipitation L-moment ratios (LMRs) and September 5-day low-flow LMRs ( τ 2 -Precipitation and τ 2 -Discharge: R2 = 0.675, p-values < 0.001; τ 3 -Precipitation and τ 3 -Discharge: R2 = 0.925, p-value for slope < 0.001, intercept not significant with p = 0.451, assuming α = 0.05 and a 31-year RWLM), which we later refine and use for prediction within our MLR algorithm. The methodology, applied to the Goat River near Creston, British Columbia, aids in understanding the implications of climate change on water resources, particularly for the yaqan nuʔkiy First Nation. We find that future low-flows under climate change will be outside the Natural Range of Variability (NROV) simulated from historical records (assuming a constant PD). This study provides insights that may help in adaptive water management strategies necessary to help preserve Indigenous cultural rights and practices and to help sustain fish and fish habitat into the future. [ABSTRACT FROM AUTHOR]

Abstract Monthly precipitation data from 58 synoptic stations throughout Botswana, spanning 1981–2016, were used in this study. The data were examined using multivariate analysis to determine regions exhibiting distinct precipitation variability patterns and regimes. To accomplish this, the T-mode of principal component analysis was applied to the correlation matrix of the data. Based on the maximum loading values of the rotational principal component scores, the T-mode indicated three separate subregions with varying precipitation patterns over time. Four clusters with distinct rainfall patterns were identified when cluster analysis was performed on the principal component scores. An assessment of the homogeneity of the clusters was performed using L-moment’s heterogeneity measure (H). Statistical analysis was employed to model annual rainfall data using five commonly used rainfall analysis probability distribution functions: normal, lognormal, gamma, Weibull, and Gumbel. The probability distributions with the greatest fit were determined based on the maximum overall score, which was calculated by adding the individual point scores of three chosen goodness-of-fit tests. Each cluster exhibited distinct probability distribution functions, with the gamma, Gumbel, lognormal, and Weibull distributions providing the most accurate descriptions.

Effective forest management is essential for mitigating climate change effects. This is why understanding forest growth dynamics is critical for its sustainable management. Thus, characterizing forest plot deadwood levels is vital for understanding forest dynamics, and for assessments of biomass, carbon stock, and biodiversity. For the first time, this study used the leaf area index (LAI) and L-moments to characterize and model forest plot deadwood levels in the Bavarian Forest National Park from airborne laser scanning (ALS) data. This study proposes methods that can be tested for forests, especially those in temperate climates with frequent cloud coverage and limited access. The proposed method is practically significant for effective planning and management of forest resources. First, plot decay levels were characterized based on their canopy leaf area density (LAD). Then, the deadwood levels were modeled to assess the relationships between the vegetation area index (VAI), gap fraction (GF), and the third L-moment ratio (T3). Finally, we tested the rule-based methods for classifying plot decay levels based on their biophysical structures. Our results per the LAD vertical profiles clearly showed the declining levels of decay from Level 1 to 5. Our findings from the models indicate that at a 95% confidence interval, 96% of the variation in GF was explained by the VAI with a significant negative association (VAIslope = −0.047; R2 = 0.96; (p < 0.001)), while the VAI explained 92% of the variation in T3 with a significant negative association (VAIslope = −0.50; R2 = 0.92; (p < 0.001)). Testing the rule-based methods, we found that the first rule (Lcv = 0.5) classified Levels 1 and 2 at (Lcv < 0.5) against Levels 3 to 5 at (Lcv > 0.5). However, the second rule (Lskew = 0) classified Level 1 (healthy plots) as closed canopy areas (Lskew < 0) against Levels 2 to 5 (deadwood) as open canopy areas (Lskew > 0). This approach is simple and more convenient for forest managers to exploit for mapping large forest gap areas for planning and managing forest resources for improved and effective forest management. [ABSTRACT FROM AUTHOR]

Drought research is needed to understand the complex nature of drought phenomena and to develop effective management and mitigation strategies accordingly. This study presents a comprehensive regional frequency analysis (RFA) of 12-month meteorological droughts in the Kızılırmak Basin of Turkey using the L-moments approach. For this purpose, monthly precipitation data from 1960 to 2020 obtained from 22 meteorological stations in the basin are used. In the drought analysis, the Standard Precipitation Index (SPI), Z-Score Index (ZSI), China-Z Index (CZI) and Modified China-Z Index (MCZI), which are widely used precipitation-based indices in the literature, are employed. Here, the main objectives of this study are (i) to determine homogeneous regions based on drought, (ii) to identify the best-fit regional frequency distributions, (iii) to estimate the maximum drought intensities for return periods ranging from 5 to 1000 years, and (iv) to obtain drought maps for the selected return periods. The homogeneity test results show that the basin consists of a single homogeneous region according to the drought indices considered here. The best-fit regional frequency distributions for the selected drought indices are identified using L-moment ratio diagrams and ZDIST goodness-of-fit tests. According to the results, the best-fit regional distributions are the Pearson-Type 3 (PE3) for the SPI and ZSI, generalized extreme value (GEV) for the CZI, and generalized logistic distribution (GLO) for the MCZI. The drought maps obtained here can be utilized as a useful tool for estimating the probability of drought at any location across the basin, even without enough data for hydrological research. [ABSTRACT FROM AUTHOR]

In a recent paper, the unit-Gompertz (UG) distribution has been introduced and some of its properties have been studied. In a follow up paper, some of the subtle errors in the original paper have been corrected and some other interesting properties of this new distribution have been studied. In the present work, some more important properties are investigated. Moreover, to the best of our knowledge, no characterization results on this distribution have appeared in the literature. These are addressed in the present paper. [ABSTRACT FROM AUTHOR]

Monthly precipitation data from 58 synoptic stations throughout Botswana, spanning 1981–2016, were used in this study. The data were examined using multivariate analysis to determine regions exhibiting distinct precipitation variability patterns and regimes. To accomplish this, the T-mode of principal component analysis was applied to the correlation matrix of the data. Based on the maximum loading values of the rotational principal component scores, the T-mode indicated three separate subregions with varying precipitation patterns over time. Four clusters with distinct rainfall patterns were identified when cluster analysis was performed on the principal component scores. An assessment of the homogeneity of the clusters was performed using L-moment's heterogeneity measure (H). Statistical analysis was employed to model annual rainfall data using five commonly used rainfall analysis probability distribution functions: normal, lognormal, gamma, Weibull, and Gumbel. The probability distributions with the greatest fit were determined based on the maximum overall score, which was calculated by adding the individual point scores of three chosen goodness-of-fit tests. Each cluster exhibited distinct probability distribution functions, with the gamma, Gumbel, lognormal, and Weibull distributions providing the most accurate descriptions. [ABSTRACT FROM AUTHOR]

There is considerable interest in identifying and locating natural forests as accurately as possible, because they are deemed essential in preventing biodiversity loss. In the boreal region, natural forests contain a substantial amount of dead wood and exhibit considerable variation in tree age, size, and species composition. However, it is difficult to define natural forests in a quantitative manner. This is an issue, for example, in the Finnish national forest inventory. If naturalness could be related to the metrics derived from tree measurements, it would be easier to locate natural forests based on the inventory data. In this study, we investigated the value of metrics computed from tree locations and tree sizes for the characterization of a key aspect of naturalness, namely, structural naturalness as defined in the Finnish national forest inventory. We used L-moments, Gini coefficient, Lorenz asymmetry, and interquartile range to quantify the variations in tree size at the plot level. We summarized the spatial pattern of trees with a spatial aggregation index. We compared the structural metrics, species proportions, and stand age using the classes of structural naturalness described in the Finnish national forest inventory, which have been determined in the field without strict numerical rules. These categories are 'natural', 'near-natural', and 'non-natural'. We found that the forests evaluated as structurally natural had larger variations in tree size and species composition and showed a more clustered spatial pattern of trees on average, although the variation in the structural metrics was considerable in all three classes. In addition, we used the structural metrics to predict naturalness by employing a random forest algorithm. Based on the structural metrics, it was possible to obtain high precision in the classification only if we simultaneously accepted low recall, and vice versa; the link between the inspected metrics and naturalness evaluated in the field was weak. The stand age separated the three classes more clearly and it also improved the classification. [ABSTRACT FROM AUTHOR]

The Two-Component Extreme Value (TCEV) distribution is traditionally known as the exact distribution of extremes arising from Poissonian occurrence of a mixture of two exponential exceedances. In some regions, flood frequency is affected by low-frequency (decadal) climate fluctuations resulting in wet and dry epochs. We extend the exact distribution of extremes approach to such regions to show that the TCEV arises as the distribution of annual maximum floods for Poissonian occurrences and (at least two) exponential exceedances. A case study using coastal basins in Queensland and New South Wales (Australia) affected by low-frequency climate variability, shows that the TCEV produces good fits to the marginal distribution over the entire range of observed values without the explicit need to resort to climate covariates and removal of potentially influential low values. Moreover, the TCEV reproduces the observed dog-leg, a key signature of different flood generation processes. A literature review shows that the assumptions underpinning the TCEV are conceptually consistent with available evidence on climate and flood mechanisms in these basins. We provide an extended domain of the TCEV distribution in the L-moment ratio diagram to account for the wider range of parameter values encountered in the case study and show that for all basins, L-skew and L-kurtosis fall within the extended domain of the TCEV. [ABSTRACT FROM AUTHOR]

Copyright of Dokuz Eylul University Muhendislik Faculty of Engineering Journal of Science & Engineering / Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi is the property of Dokuz Eylul Universitesi Muhendislik Fakultesi Fen ve Muhendislik Dergisi and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents an application of L-moments and respective L-moment ratio diagrams (LMRD) to the task of control performance assessment (CPA). An L-moment ratio diagram is a graphical approach to the visualization of statistical properties for a given time series. Moreover, it enables comparing various data, showing their similarities and homogeneity. Simultaneously, CPA aims at measuring the control loop quality, supporting decision-making about their tuning and maintenance. This paper shows that control system quality can be efficiently visualized using LMRDs. The method was analyzed using simulations and further validated at a real chemical engineering industrial ammonia synthesis plant. [ABSTRACT FROM AUTHOR]

In this paper, we derive the exact expressions, as well as recurrence relations, for the single and product moments of the order statistics (OSs) and record values of the Topp-Leone Lomax (TLLo) distribution proposed by Oguntunde et al. (Wirel Person Commun 109:349–360, 2019). In addition, we study the corresponding L-moments. We estimate the distribution parameters through these L-moments and compare our results to those obtained in other models. Subsequently, motivated by the study of Okorie and Nadarajah (Wirel Person Commun 115:589–596, 2020), we fit the flood level data to the TLLo distribution. Finally, we reveal a relationship between the entropy and the upper and lower record values, as well as OSs. [ABSTRACT FROM AUTHOR]

To improve the estimate of the shape of a reaction-time distribution, it is sometimes desirable to combine several samples, drawn from different sessions or different subjects. How should these samples be combined? This paper provides an evaluation of four combination methods, two that are currently in use (the bin-means histogram, often called "Vincentizing", and quantile averaging) and two that are new (linear-transform pooling and shape averaging). The evaluation makes use of a modern method for describing the shape of a distribution, based on L-moments, rather than the traditional method, based on central moments. Also provided is an introduction to shape descriptors based on L-moments, whose advantages over central moments—less biased and less sensitive to outliers—are demonstrated. Whether traditional or modern shape descriptions are employed, the combination methods currently in use, especially bin-means histograms, based on averaged bin means, prove to be substantially inferior to the new methods. Averaged bin-means themselves are less deficient when estimating differences between distribution shapes, as in delta plots, but are nonetheless inferior to linear-transform pooling. [ABSTRACT FROM AUTHOR]

The use of machine learning (ML) and its applications is one of the leading research areas nowadays. Neural networks have recently gained enormous popularity and many works in various fields use them in the hope of improving previous results. The application of the artificial intelligence (AI) methods and the rationale for this decision is one issue, but the assessment of such a model is a completely different matter. People mostly use mean square error or less often mean absolute error in the absolute or percentage versions. One should remember that an error does not equal an error and a single value does not provide enough knowledge about the causes of some behavior. Proper interpretation of the results is crucial. It leads to further model improvement. It might be challenging, but allows us to obtain better and more robust solutions, which ultimately solve real-life problems. The ML model assessment is the multicriteria task. A single measure delivers only a fraction of the picture. This paper aims at filling that research gap. Commonly used integral measures are compared with alternative measures like factors of the Gaussian and non-Gaussian statistics, robust statistical estimators, tail index and the fractional order. The proposed methodology delivers new single-criteria indexes or the multicriteria approach, which extend the statistical concept of the moment ratio diagram (MRD) into the index ratio diagram (IRD). The proposed approach is validated using real data from the Full Truck Load cost estimation example. It compares 35 different ML regression algorithms applied to that task. The analysis gives an insight into the properties of the selected methods, enables their comparison and homogeneity analysis and ultimately leads towards constructive suggestions for their eventual proper use. The paper proposes new indexes and concludes that correct selection of the residuum analysis methodology makes the assessment and the ML regression credible. [ABSTRACT FROM AUTHOR]

Copyright of Environmental & Social Management Journal / Revista de Gestão Social e Ambiental is the property of Environmental & Social Management Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study developed a novel approach that integrated climate model selection and multi-model ensemble (MME) construction to effectively represent model uncertainties and, consequently, improve consistency in the evaluation of changes to extreme rainfall in different scenarios. Our focus was to combine 10 regional climate model (RCM) simulations, forced by two global climate models (GCM), especially for estimation of design rainfall in a changing climate. We hypothesized that the natural variability and statistically higher moment attributes in the extreme rainfall simulations from RCMs were not fully preserved. Therefore, the MME approach could be more effective in climate change studies, largely due to the use of multiple climate models. First, an experimental study was proposed to validate the efficacy of the proposed modeling framework approach adopting L-moments to quantify relative importance among climate models and their use for representing natural variability in the MME construction. The proposed approach was then applied to climate change scenarios collected from multiple RCMs for the Han-River watershed during both historical (1981–2005) and future (2006–2 100) periods. The results showed that the climate model selection informed by natural variability demonstrated better performance, representing nearly identical distribution to the observed annual maximum rainfall (AMR) in the Han River watershed. The range of the selected scenario was relatively narrower than that of all the scenarios, and the change rate was more consistent with the limited zero crossing, reflecting improvement in both model performance and consistency over historical and future periods, respectively. The change rate of the MME under RCP8.5 appeared to be an approximately 20% increase for the near (2011–2040) and far (2071–2 100) future, and the degree of increase in the rate for the mid-future (2041–2070) was slightly lower than that for the other periods, with increase of approximately 10%.

Extreme rainfall events are occasional, and understanding their intensity and frequency is important for long-term planning and for public safety. The current study aims to investigate the stability of extreme precipitation events in different regions of Pakistan, their independence and the uniformity of their occurrence. A rainfall frequency analysis (RFA) was conducted based on information from 8 weather stations namely, the distribution and moments L of the annual maximum precipitation in Pakistan were investigated; Using goodness-of-fit criteria, the study determined the possible distribution of precipitation. Relatively Absolute Error (RAE) results are based on the most appropriate GUM distribution, revealed that the Sialkot, Multan, Faisalabad and DI Khan stations produce very low errors (0.266, 0.847, 0.075, 0.856, 1.671, 2.522, 3.659, 4.524). It was found that the most suitable distribution is LN distribution for Peshawar, Sibbi and Karachi Stations. The GEV distribution also performs well with small errors for various return periods (0.266, 0.847, 0.075, 0.856, 1.671, 2.522, 3.659, 4.524), corresponding to the return periods 2, 5, 25, 50, 100, 200, 500 and 1000 years. In contrast, P3 has the advantage of a return period of 10 years for all stations, as they all produce similar results for this particular return period. The current research provides valuable insights into estimating extreme rainfall at stations where rainfall data are available.

Here, we investigate the use of rolling-windowed L-moments (RWLMs) and L-moment ratio diagrams (LMRDs) combined with a Multiple Linear Regression (MLR) machine learning algorithm to model non-stationary low-flow hydrological extremes with the potential to simultaneously understand time-variant shape, scale, location, and probability distribution (PD) shifts under climate change. By employing LMRDs, we analyse changes in PDs and their parameters over time, identifying key environmental predictors such as lagged precipitation for September 5-day low-flows. Our findings indicate a significant relationship between total August precipitation L-moment ratios (LMRs) and September 5-day low-flow LMRs (τ2-Precipitation and τ2-Discharge: R2 = 0.675, p-values < 0.001; τ3-Precipitation and τ3-Discharge: R2 = 0.925, p-value for slope < 0.001, intercept not significant with p = 0.451, assuming α = 0.05 and a 31-year RWLM), which we later refine and use for prediction within our MLR algorithm. The methodology, applied to the Goat River near Creston, British Columbia, aids in understanding the implications of climate change on water resources, particularly for the yaqan nuʔkiy First Nation. We find that future low-flows under climate change will be outside the Natural Range of Variability (NROV) simulated from historical records (assuming a constant PD). This study provides insights that may help in adaptive water management strategies necessary to help preserve Indigenous cultural rights and practices and to help sustain fish and fish habitat into the future.

Several periods of drought in the 21st century have severely affected large parts of Europe and caused considerable economic losses, particularly in the agricultural and energy sectors. While rainfall deficits are one of the main causes of droughts, high temperatures in the summer months exacerbate their development, which can have devastating consequences. This was the case in 2022, when long dry spells were accompanied by several heat waves. In this study, climatological drought monitoring using the Standardized Precipitation Evapo-transpiration Index (SPEI) is analyzed with the primary goal of finding the best theoretical distribution for adjusting the water balance (defined as the difference between precipitation and potential evapotranspiration) in Croatia before the index is officially introduced into the operational drought monitoring. Although the SPEI is widely used for drought monitoring, the underlying theoretical distribution of the water balance may differ between regions. The study is based on monthly precipitation amounts and monthly mean values of daily minimum and maximum temperatures observed at 31 main meteorological stations for the period 1961--2022. The analysis is carried out for different time scales, ranging from 1 to 24 months. Among the five distributions considered, a generalized logistic distribution with three parameters (GLO) proves to be the most appropriate. There is general agreement between SPEI and SPI time series, both in terms of sign and intensity. However, in periods with a light to moderate lack of precipitation and high air temperatures, a tendency towards higher drought intensity prevails in the SPEI. A comparative analysis of the 2022 drought in Croatia confirmed the ability of the SPEI to detect a drought earlier than the SPI, which also suggests that a larger area of the country was affected by the drought due to consistent air temperature excesses. [ABSTRACT FROM AUTHOR]

In this article, we propose a new class of distributions defined by a quantile function, which is the sum of the quantile functions of the Power and Weibull distributions. Various distributional properties and reliability characteristics of the class are discussed. To examine the usefulness of the model, the model is applied to a real life datasets. Parameters are estimated using maximum likelihood estimation technique. [ABSTRACT FROM AUTHOR]

Effective forest management is essential for mitigating climate change effects. This is why understanding forest growth dynamics is critical for its sustainable management. Thus, characterizing forest plot deadwood levels is vital for understanding forest dynamics, and for assessments of biomass, carbon stock, and biodiversity. For the first time, this study used the leaf area index (LAI) and L-moments to characterize and model forest plot deadwood levels in the Bavarian Forest National Park from airborne laser scanning (ALS) data. This study proposes methods that can be tested for forests, especially those in temperate climates with frequent cloud coverage and limited access. The proposed method is practically significant for effective planning and management of forest resources. First, plot decay levels were characterized based on their canopy leaf area density (LAD). Then, the deadwood levels were modeled to assess the relationships between the vegetation area index (VAI), gap fraction (GF), and the third L-moment ratio (T3). Finally, we tested the rule-based methods for classifying plot decay levels based on their biophysical structures. Our results per the LAD vertical profiles clearly showed the declining levels of decay from Level 1 to 5. Our findings from the models indicate that at a 95% confidence interval, 96% of the variation in GF was explained by the VAI with a significant negative association (VAIslope = −0.047; R2 = 0.96; (p < 0.001)), while the VAI explained 92% of the variation in T3 with a significant negative association (VAIslope = −0.50; R2 = 0.92; (p < 0.001)). Testing the rule-based methods, we found that the first rule (Lcv = 0.5) classified Levels 1 and 2 at (Lcv < 0.5) against Levels 3 to 5 at (Lcv > 0.5). However, the second rule (Lskew = 0) classified Level 1 (healthy plots) as closed canopy areas (Lskew < 0) against Levels 2 to 5 (deadwood) as open canopy areas (Lskew > 0). This approach is simple and more convenient for forest managers to exploit for mapping large forest gap areas for planning and managing forest resources for improved and effective forest management.

Drought research is needed to understand the complex nature of drought phenomena and to develop effective management and mitigation strategies accordingly. This study presents a comprehensive regional frequency analysis (RFA) of 12-month meteorological droughts in the Kızılırmak Basin of Turkey using the L-moments approach. For this purpose, monthly precipitation data from 1960 to 2020 obtained from 22 meteorological stations in the basin are used. In the drought analysis, the Standard Precipitation Index (SPI), Z-Score Index (ZSI), China-Z Index (CZI) and Modified China-Z Index (MCZI), which are widely used precipitation-based indices in the literature, are employed. Here, the main objectives of this study are (i) to determine homogeneous regions based on drought, (ii) to identify the best-fit regional frequency distributions, (iii) to estimate the maximum drought intensities for return periods ranging from 5 to 1000 years, and (iv) to obtain drought maps for the selected return periods. The homogeneity test results show that the basin consists of a single homogeneous region according to the drought indices considered here. The best-fit regional frequency distributions for the selected drought indices are identified using L-moment ratio diagrams and ZDIST goodness-of-fit tests. According to the results, the best-fit regional distributions are the Pearson-Type 3 (PE3) for the SPI and ZSI, generalized extreme value (GEV) for the CZI, and generalized logistic distribution (GLO) for the MCZI. The drought maps obtained here can be utilized as a useful tool for estimating the probability of drought at any location across the basin, even without enough data for hydrological research.

Statistical analysis of extreme events such as flood events is often carried out to predict large return period events. The behaviour of extreme events not only involves heavy-tailed distributions but also skewed distributions, similar to the four-parameter Kappa distribution (K4D). In general, this covers many extreme distributions such as the generalized logistic distribution (GLD), the generalized extreme value distribution (GEV), the generalized Pareto distribution (GPD), and so on. To utilize these distributions, we have to estimate parameters accurately. There are many parameter estimation methods, for example, Method of Moments, Maximum Likelihood Estimator, L-Moments, or partial L-Moments. Nowadays, no researchers have applied the partial L-Moments method to estimate the parameters of K4D. Therefore, the objective of this paper is to derive the partial L-Moments (PL-Moments) for K4D, namely the PL-Moments of the K4D in order to estimate hydrological extremes from censored data. The findings of this paper are formulas of parameter estimation for K4D based on the PL-Moments approach. We have derived the Partial Probability-Weighted Moments (PPWMs) of the K4D (β'r) and derive the estimation of parameters when separated by shape parameters (k,h) conditions i.e., case k>-1 and h>0, case k>-1 and h=0 and case -1

Estimation of return levels, based on extreme-value distributions, is of importance in the earth and environmental sciences. The selection of an appropriate probability distribution is crucial. The Wakeby distribution has shown to be an interesting alternative. By simulation studies, we investigate by various means of minimum distance to distinguish between common distributions when modelling extreme events in hydrology. Estimation of parameters is performed by L-moments. Moreover, time series of annual maximum floods from major unregulated rivers in Northern Sweden were analysed with respect to fitting an appropriate distribution. The results of the simulation study shows that the Wakeby distribution has the best fit of the tail for a wide range of sample sizes. For the analysis of extreme floods, the Wakeby distribution is in the majority of cases the best fit by means of minimum distance. However, when considering estimation of return levels by competing distributions, results can vary considerably for longer return periods.

Nadarajah and Haghighi [1] introduced the alternative to the gamma, Weibull and exponentiated exponential distribution with zero mode and allows for increasing, decreasing and constant hazard rates as an extension of exponential distribution. Later Lemonte [2] described the three parameters as exponentiated of the distribution of Nadarajah and Haghighi [1] and given the name as exponentiated Nadarajah–Haghighi (ENH) distribution. Lemonte [2] obtained the rational properties and application of the ENH distribution as moments, entropies, maximum likelihood estimation and stress–strength estimation etc. In this paper, we have obtained the exact expression for single and product moments of order statistics arising from ENH distribution. By using these expressions, we have computed the means of order statistics for and for arbitrarily chosen parameter values. Furthermore, the practical application of our findings was well-suited by the linear combination of these order moments as L-moments. Finally, we interpreted the findings and their future work. [ABSTRACT FROM AUTHOR]

In this paper, we derive the L-moments for some distributions, such as logistic, generalized logistic, doubly truncated logistic, and doubly truncated generalized logistic distributions. We also establish some new axioms and identities, including recurrence relations satisfied by the L-moment from the underlying derivations. In addition, we establish some new general recurrence relations satisfied by the L-moment from any distribution. [ABSTRACT FROM AUTHOR]

The effects of climate change have posed several threats and far more than the effects on Pakistan as the temperature is constantly rising and this could lead to an increase in the severity of extreme events. This study analyzed the climate change's impact on climatic regions that are established by using the data of precipitation and temperature for 55 meteorological stations in Pakistan based on Reconnaissance Drought Index. For the construction of homogeneous climatic regions (HCRs), two statistical methods were integrated. First, cluster analysis was employed to identify climatic regions (CRs) using site characteristics of the stations, which gave five climatic regions (CRs). Second, heterogeneity measure and discordancy measure were used based on L-moment approach and regional adjustments to satisfy the homogeneity of HCRs. These HCRs were evaluated on REMO model (a regional climate model), for the baseline period of 1976–2005. To assess the impacts of climate change, HCRs were constructed, and climate projections were developed under the RCP 4.5 and RCP 8.5 for twenty first century. The results of HCRs show that some stations interchanged with other groups under both future scenarios due to changes in temperature and precipitation. It is observed that the maximum and minimum temperature will highly increase in the future and major increase in temperature is projected in 2071–2100 with RCP 4.5 and 8.5. This study will assist in the short and long-term planning of climate change, irrigation, water management, hydropower etc. in the country. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of distributions with bilinear mean residual quantile function. We study various distributional properties and reliability characteristics of the proposed class. Characterizations of the model are presented and the method of L-moments is employed to estimate parameters of the class of distributions. Finally, we illustrate the usefulness of the proposed claim to a real data set. [ABSTRACT FROM AUTHOR]

In this paper, a convenient and parsimonious family of the quantile functions is proposed for modeling time-to-event data. Detailed mathematical arguments are presented for deriving the explicit expressions of the quantile density, quantile hazard and quantile mean remaining life functions. Their functional properties are also explored. Some important members of the family are provided. A special case, the so-called additive power logarithmic quantile family, is discussed with detailed properties, parameter estimation and application to time-to-event data. Measures of skewness and kurtosis for the proposed quantile function are derived. Important statistical measures useful for reliability analysis are also provided with their explicit expressions. Stochastic ordering, tail weight and order statistics are also discussed. L-moments are explicitly derived for the proposed quantile function. Estimation is approached using the likelihood function and percentiles. A real data set consists of times between occurrence of the coal-mining accidents is analyzed for illustration purposes. [ABSTRACT FROM AUTHOR]

This paper introduces a new family of distributions defined in terms of quantile function. The quantile function introduced here is the sum of quantile functions of life time distributions called Burr III and Weibull. Different distributional characteristics and reliability properties are included in the study. Method of Least Square and Method of L-moments are applied to estimate the parameters of the model. Two real life data sets are used to illustrate the performance of the model.

This paper presents an application of L-moments and respective L-moment ratio diagrams (LMRD) to the task of control performance assessment (CPA). An L-moment ratio diagram is a graphical approach to the visualization of statistical properties for a given time series. Moreover, it enables comparing various data, showing their similarities and homogeneity. Simultaneously, CPA aims at measuring the control loop quality, supporting decision-making about their tuning and maintenance. This paper shows that control system quality can be efficiently visualized using LMRDs. The method was analyzed using simulations and further validated at a real chemical engineering industrial ammonia synthesis plant.

Estimation of the population variance is of major concern in numerous examinations and ratio estimators are mainstream choices for it. It is a typical practice to utilize conventional central moments to construct variance estimators utilizing auxiliary information. However, conventional central moments give equal weight to each observation and hence highly affected by extreme values. For solving this issue, some recent developments are available in literature based on non-conventional/robust characteristics (inter-decile range, mid-range, etc.) of an auxiliary variable with conventional central moments under a simple random sampling scheme. This article initially, defines a family of ratio type variance estimators based on an adaptation of existing estimators with conventional central moments and non-conventional/robust characteristics of the auxiliary variable under a stratified random sampling scheme. After that, a novel family of variance estimators is proposed, in the presence of extreme values. The novel family of variance estimators is based on L-moments and calibration approach with some suitable constraints which can provide enhance the estimation of the population variance. We utilize L-moments characteristics (L-location, L-scale, and L-CV) for the purposes of the article. The variance expression of the novel family is also provided. Empirical illustrations are done using real and artificial data sets. The percentage relative efficiency is used for assessing the performances of adapted and novel families of estimators. [ABSTRACT FROM AUTHOR]

In this study, a regional rainfall frequency analysis has been conducted for the Lower Brahmaputra Basin in India, and regional rainfall intensity-duration-frequency curves are generated. Two sets of data have been used in this study—annual maximum series (AMS) and partial duration series (PDS). The discordancy measure (Di) was used to assess each of these 12 data sets from the Lower Brahmaputra Basin. For both data sets, it was verified that all the 12 sites form a homogeneous zone using the heterogeneity measure (H), which was based on the L-moments technique. The generalised extreme value, generalised logistic, generalised Pareto, lognormal, and Pearson Type III frequency distributions were considered as candidate distributions in this study. The generalised extreme value distribution has been recognised as the best-fit distribution for the region based on AMS, whereas the generalised Pareto distribution has been identified as the best-fit distribution for the region based on PDS, using the L-moment goodness of fit test measure. Then using the regional frequency relationship for the best fit distribution for the region, the IDF curves for this region have been constructed. Finally, rainfall IDF relationships were found out for the region based on three general IDF relationships—the original Kothyari and Garde IDF equation for India, the updated Kothyari and Garde IDF equation and the Sherman IDF equation. [ABSTRACT FROM AUTHOR]

With the advent of continuous health monitoring with wearable devices, users now generate their unique streams of continuous data such as minute-level step counts or heartbeats. Summarizing these streams via scalar summaries often ignores the distributional nature of wearable data and almost unavoidably leads to the loss of critical information. We propose to capture the distributional nature of wearable data via user-specific quantile functions (QF) and use these QFs as predictors in scalar-on-quantile-function-regression (SOQFR). As an alternative approach, we also propose to represent QFs via user-specific L-moments, robust rank-based analogs of traditional moments, and use L-moments as predictors in SOQFR (SOQFR-L). These two approaches provide two mutually consistent interpretations: in terms of quantile levels by SOQFR and in terms of L-moments by SOQFR-L. We also demonstrate how to deal with multi-modal distributional data via Joint and Individual Variation Explained using L-moments. The proposed methods are illustrated in a study of association of digital gait biomarkers with cognitive function in Alzheimers disease. Our analysis shows that the proposed methods demonstrate higher predictive performance and attain much stronger associations with clinical cognitive scales compared to simple distributional summaries. [ABSTRACT FROM AUTHOR]

This paper presents an application of L-moment statistics and the respective L-moment ratio diagrams (LMRD) to assess control performance, in particular, in terms of control system sustainability. L-moment diagrams are common in extreme events analysis and are considered a very powerful tool in this field at the regional level. Control system assessment is a well-established research area that investigates approaches and methodologies for measuring the quality of control systems. Statistical moments can be used to assess the effectiveness of control systems. The same principle applies to L-moments, with a possible further application to the assessment of control system robustness. The incorporation of the time impact into the analysis allows us to examine the evolution of control systems. In this context, measuring sustainability is only one step away. In this research, L-moments and L-moment ratio diagrams are used to assess the quality of PID-based control systems. In addition, the evolution of their performance over time is depicted visually. Moreover, a robust discordance measure is proposed to measure the robustness, evolution, and sustainability of control systems. The proposed approach is successfully validated using real industrial data obtained from PID basic regulatory control within the hierarchical advanced process control (APC) structure of a large ammonia production plant. [ABSTRACT FROM AUTHOR]

The Tigris and Euphrates basin is a challenging watershed because its water resources are critical for five countries. Therefore, this research analyzed and estimated the low flow index and its risk of occurrence. Based on 30 unregulated stations in the upper Tigris and Euphrates basin, different low flow indexes were estimated. A multivariate and hybrid principle component regression (PCR) regional model was used to assign the relationship between basin characteristics and low flow indexes in the homogeneous regions. The model performance showed that the principle component regression outperformed the regression models. The jackknife procedure indicated that the model performance for short-duration low flows is weak, but it is relatively good for long-duration low flows. This study suggests that hydrologic drought of the Tigris and Euphrates basin should be investigated more carefully for better water resources management in the changing socio-environmental system of the Middle East. [ABSTRACT FROM AUTHOR]

In water resources management, environmental and ecological studies, estimation of design streamflow is often needed. For gauged catchments, at-site flood frequency analysis is used for this purpose; however, for ungauged catchments, regional flood frequency analysis (RFFA) is the preferred method. RFFA attempts to transfer flood characteristics from gauged to ungauged catchments based on the assumption of regional homogeneity. A bibliometric analysis on RFFA is presented here using Web of Science (WoS) and Scopus databases. A total of 626 articles were selected from these databases. From the bibliometric analysis, it has been found that Journal of Hydrology and Water Resources Research are the two leading journals reporting RFFA research. In RFFA research, leading countries include Canada, USA, UK, Italy and Australia. In terms of citations, the top performing researchers are Ouarda T, Burn D, Rahman A, Haddad K and Chebana F. Future research should be directed towards the identification of homogeneous regions, application of efficient artificial intelligence (AI)-based RFFA models, incorporation of climate change impacts and uncertainty analysis. [ABSTRACT FROM AUTHOR]

Leveraging the properties of the first three linear moments (L-moments), this study proposes an effective normal transformation for structural reliability analysis considering correlated input random variables, in which the admissible range of the initial correlation matrix when employing this transformation is also presented. Subsequently, a practical procedure for structural reliability analysis, grounded in the proposed transformation and first-order reliability method (FROM), is proposed, accommodating instances wherein the joint probability density functions (PDFs) or marginal PDFs of the relevant random variables remain unknown. In comparison to the technique premised on the first three central moments (C-moments), the proposed method, based on the first three L-moments, exhibits a more extensive applicability. Various practical scenarios showcase the method's effectiveness and precision in calculating the structural reliability index, considering diverse distributions, numerous variables, and complex structures. [ABSTRACT FROM AUTHOR]

In reliability studies, the data is often truncated and hence the residual random variable plays a vital role in the modelling and analysis of lifetime data. Like various reliability measures such as hazard rate, mean residual life function, variance residual life function, the residual coefficient of variation is also an important tool considered by many. In this paper, we study a quantile version of coefficient of variation of residual life, an alternative to the traditional distribution function measure. We study various properties of it and obtain characterizations based on some well-known probability models. We introduce a class of distributions with linear quantile-based residual coefficient of variation and study their basic reliability properties. We also obtain some stochastic comparison and aging properties using quantile-based residual coefficient of variation. The L-moment method of estimation for the class of distributions with linear quantile-based residual coefficient of variation has also been illustrated using two real data sets. [ABSTRACT FROM AUTHOR]

Extreme events gives rise to outrageous results in terms of population-related parameters and their estimates are usually done using traditional moments. Traditional moments are usually affected by extreme observations. This study aims to propose some new calibration estimators considering the L-Moments scheme for variance, which is one of the most important population parameters. a number of suitable calibration constraints under double stratified random sampling were defined for these estimators. The proposed estimators, which were based on L-Moments, were relatively more robust despite extreme values. The empirical efficiency of the proposed estimators was also assessed through simulation. Covid-19 pandemic data from January 22, 2020 to August 23, 2020 was taken into account in the simulation study. [ABSTRACT FROM AUTHOR]

Floods are one of the most frequent and destructive natural events which lead to lots of human and financial losses with damage to the houses, farms, roads, and other buildings. Intensity–duration–frequency (IDF) curves are the main and practical tools that have been used for flood control studies, including the design of the water structures. In many cases, there is no measuring device at the desired place, or their information is not helpful if there is any available. In this case, it is not possible to extract these curves through conventional methods. Regionalizing the IDF curves is a method that has solved the issues mentioned in the common methods. In this research, the regionalized IDF curves are extracted in Khuzestan province, Iran using 21 rain gauge stations through L-moments and neural gas networks. Clustering is one of the most effective steps and a prerequisite for regional frequency analysis (RFA) that divides the region and existing stations into hydrologically homogenous regions. In this study, clustering is done using two new models named neural gas (NG) and growing neural gas (GNG) network. Comparing the regional IDF curves with at-site curves, it was found that neural gas network models had a more accurate performance and higher efficiency, so they had the lowest estimate error amount among other models. Also, due to the acceptable difference between regional and at-site curves, the efficiency of L-moments in RFA was evaluated as appropriate. [ABSTRACT FROM AUTHOR]

The global mean surface temperature is rising and under climate change it is expected to increase in the future. The changes are not uniform across the world and the impact assessment at a regional level is, thus, a necessity. Bangladesh, a tropical low-lying monsoon region, is greatly at risk under climate change. However, no attempt has been carried out to assess the changes in frequency of extreme temperatures (return period values) under the backdrop of climate change which is required in practical applications. The aim of this study is to investigate the changes in temperature extremes: maximum (Tx) and minimum (Tn) at the daily time scale under climate change in Bangladesh. The multi-model ensemble methodology comprised of five general circulation models and two emission scenarios from CMIP6 framework was used to evaluate the impact in two future time horizons: 2021–2060 and 2061–2100. The L-moment based frequency analysis with annual maxima (minima) data was used to quantify extreme temperatures in terms of return levels. With this approach, the identification of a probability distribution is one important aspect which is investigated in this study. We have found that the generalized normal (GNO) distribution is quite appropriate of describing the temperature extremes. There is a significant increase in location parameter which signifies a uniform shift for the extreme tail of the distribution. There are no appreciable overall changes in scale and shape parameter. The temperature extremes (both Tx and Tn) are expected to increase noticeably compared to the present observed condition. There is a tendency to have a greater estimate of extremes in the far future than the near future. The greater estimate is also perceived under the high emission scenario in comparison to the medium emission scenario. The country average change in 20-year return period value of Tx by the end of this century is about 3–4.7 °C compared to the corresponding changes of 2.4 to 3.7 °C for Tn. The findings are expected to assist in the evaluation of climate change impacts and adaptation strategies in Bangladesh. [ABSTRACT FROM AUTHOR]

Reducing uncertainty in design flood estimates is an essential part of flood risk planning and management. This study presents results from flood frequency estimates and associated uncertainties for five commonly used probability distribution functions, extreme value type 1 (EV1), generalized extreme value (GEV), generalized pareto distribution (GPD), log normal (LN) and log Pearson type 3 (LP3). The study was conducted using Monte Carlo simulation (MCS) and bootstrapping (BS) methods for the 10 river catchments in eastern Australia. The parameters were estimated by applying the method of moments (for LP3, LN, and EV1) and L-moments (for GEV and GPD). Three-parameter distributions (e.g., LP3, GEV, and GPD) demonstrate a consistent estimation of confidence interval (CI), whereas two-parameter distributions show biased estimation. The results of this study also highlight the difficulty in flood frequency analysis, e.g., different probability distributions perform quite differently even in a smaller geographical area. [ABSTRACT FROM AUTHOR]

Proper flood discharge forecasting is significant for the design of hydraulic structures, reducing the risk of failure, and minimizing downstream environmental damage. The objective of this study was to investigate the application of machine learning methods in Regional Flood Frequency Analysis (RFFA). To achieve this goal, 18 physiographic, climatic, lithological, and land use parameters were considered for the upstream basins of the hydrometric stations located in Karkheh and Karun watersheds (46 stations with a statistical length of 21 years). The best Probability Distribution Function (pdf) was then determined using the Kolmogorov-Smirnov test at each station to estimate the flood discharge with a return period of 50-year using maximum likelihood methods and L-moments. Finally, RFFA was performed using a decision tree, Bayesian network, and artificial neural network. The results showed that the log Pearson type 3 distribution in the maximum likelihood method and the generalized normal distribution in the L moment method are the best possible regional pdfs. Based on the gamma test, the parameters of the perimeter, basin length, shape factor, and mainstream length were selected as the best input structure. The results of regional flood frequency analysis showed that the Bayesian model with the L moment method (R2 = 0.7) has the best estimate compared to other methods. Decision tree and artificial neural network were in the following ranks.

In this paper, we derive the L-moments for some distributions, such as logistic, generalized logistic, doubly truncated logistic, and doubly truncated generalized logistic distributions. We also establish some new axioms and identities, including recurrence relations satisfied by the L-moment from the underlying derivations. In addition, we establish some new general recurrence relations satisfied by the L-moment from any distribution.