ESTIMATION OF THE FLOOD MAXIMUM VOLUMES FOR VARIOUS DURATIONS OF THE RIVER RUNOFF AND THEIR MUTUAL DEPENDANCES: A CASE STUDY ON HRON RIVER IN SLOVAKIA

2020 ◽  
Author(s):  
Veronika Bačová Mitková ◽  
◽  
Dana Halmová ◽  
Keyword(s):  
Probability Distribution ◽  
Extreme Values ◽  
Random Variable ◽  
Distribution Functions ◽  
Mathematical Tool ◽  
Return Periods ◽  
Copula Functions ◽  
Time Duration ◽  
Positive Dependence ◽  
Log Normal

This work deals with the determination of the annual maximum discharge volumes on the Hron River for the runoff time duration t = 2, 5, 10, and 20 days. The series of 84 years (1931–2015) mean daily discharges of the Hron River at Banská Bystrica station was used as input data to calculate the maximum annual volumes of runoff of the Hron River. Subsequently, the theoretical curves of exceedance of the maximal discharge volumes were determined by the LogPearson distribution of the Type III. This type of probability distribution is used to estimate maximum (extreme) values across a range of natural processes. The results of the estimated T-year volumes by using PL III distribution were compared to other types of theoretical distribution functions used in hydrological extreme analyses in Slovakia (Gamma, Log-normal, etc.). The second part of our work was focused on the bivariate modelling of the relationship between T-year maximum volumes with different duration and peak discharges. In the case of modelling without evaluating this mutual dependence of the flood wave characteristics, they may be overestimated (in the case of the negative dependence) or underestimated (in the case of the positive dependence). The Archimedean class of copula functions was used as mathematical tool for the dependence modelling. The LP III distribution was used as marginal probability distribution function. Subsequently joint and conditional return periods of the T-year maximum annual flows and T-year maximum volumes with different time duration were calculated. The first one defines joint return periods as: the return periods using one random variable equaling or exceeding a certain magnitude and/or using another random variable equaling or exceeding another certain magnitude. The second one is conditional return periods for one random variable, given that another random variable equals or exceeds a specific magnitude.

scholarly journals Stochastic Bioimpedance-Based Channel Model of the Human Body for Galvanic Coupling

2021 ◽  
Vol 12 (1) ◽  
pp. 117-124
Author(s):  
Aaron Roopnarine ◽  
Sean A. Rocke
Keyword(s):  
Human Body ◽  
Channel Model ◽  
Random Variable ◽  
Distribution Functions ◽  
Galvanic Coupling ◽  
Body Segments ◽  
Generalized Pareto ◽  
Body Parameter ◽  
Log Normal ◽  
Body Parameters

Abstract Human body communication (HBC) uses the human body as the channel to transfer data. Extensive work has been done to characterize the human body channel for different HBC techniques and scenarios. However, statistical channel bioimpedance characterisation of human body channels, particularly under dynamic conditions, remains relatively understudied. This paper develops a stochastic fading bioimpedance model for the human body channel using Monte Carlo simulations. Differential body segments were modelled as 2-port networks using ABCD parameters which are functions of bioimpedance based body parameters modelled as random variables. The channel was then modelled as the cascade of these random 2-port networks for different combinations of probability distribution functions (PDFs) assumed for the bioimpedance-based body parameters. The resultant distribution of the cascaded body segments varied for the different assumed bioimpedance based body parameter distributions and differential body segment sizes. However, considering the distribution names that demonstrated a best fit (in the top 3 PDF rankings) with highest frequency under the varying conditions, this paper recommends the distribution names: Generalized Pareto for phase distributions and Log-normal for magnitude distributions for each element in the overall cascaded random variable ABCD matrix.

Probabilistic Carbonation Simulations in Concrete Based on Marble Powder

2020 ◽  
Vol 1013 ◽  
pp. 114-119
Author(s):  
Azhar Badaoui
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Random Variable ◽  
Carbonation Depth ◽  
Concrete Carbonation ◽  
Normal Probability ◽  
Powder Diameter ◽  
Marble Powder ◽  
Normal Probability Distribution ◽  
Log Normal

The aim of this paper is the evaluation of concrete carbonation depth from a probabilistic analysis, focusing specifically on the study of the marble powder diameters randomness effect on the reinforced concrete carbonation. Monte Carlo simulations are realized under the assumption that the marble powder diameter (Dmp) is random variable with a log-normal probability distribution.

scholarly journals Probability Distribution of Precipitation Extremes for Weather Index–Based Insurance in the Zhujiang River Basin, South China

2012 ◽  
Vol 13 (3) ◽  
pp. 1023-1037 ◽  
Author(s):  
Thomas Fischer ◽  
Buda Su ◽  
Yong Luo ◽  
Thomas Scholten
Keyword(s):  
Probability Distribution ◽  
River Basin ◽  
Distribution Functions ◽  
Precipitation Extremes ◽  
Economic Losses ◽  
Return Periods ◽  
Weather Index ◽  
Maximum Precipitation ◽  
Insurance Program ◽  
Zhujiang River

Abstract In a changing climate, understanding the frequency of weather extremes is crucial to improving the management of the associated risks. The concept of weather index–based insurance is introduced as a new approach in weather risk adaptation. It can decrease the vulnerability to precipitation extremes that cause floods and economic losses in the Zhujiang River basin. The probability of precipitation extremes is a key input and the probability distribution of annual precipitation extremes is analyzed with four distribution functions [gamma 3, generalized extreme value (GEV), generalized Pareto, and Wakeby]. Three goodness-of-fit tests (Kolmogorov–Smirnov, Anderson–Darling, and Chi Squared) are applied to the distribution functions for annual time series (1961–2007) of 192 meteorological stations. The results show that maximum precipitation and 5-day-maximum precipitation are best described by the Wakeby distribution. On a basin scale, the GEV is the most reliable and robust distribution for estimating precipitation indexes for an index-based insurance program in the Zhujiang River basin. However, each station has to be analyzed individually as GEV is not always the best-fitting distribution function. Based on the distribution functions, spatiotemporal characteristics of return periods for maximum precipitation and 5-day-maximum precipitation are determined. The return levels of the 25- and 50-yr return periods show similar spatial pattern: they are higher in the southeast and lower in the southwest of the basin. This spatial distribution is in line with the annual averages. The statistical distribution of precipitation indexes delivers important information for a theoretical weather index–based insurance program.

scholarly journals Definite Probabilities from Division of Zero by Itself Perspective

2020 ◽  
pp. 1-26
Author(s):  
Wangui Patrick Mwangi
Keyword(s):  
Probability Distribution ◽  
Negative Binomial ◽  
Random Variable ◽  
Distribution Functions ◽  
Point Of View ◽  
Basic Knowledge ◽  
Probability Distribution Functions ◽  
New Findings ◽  
Wide Range ◽  
New Finding

Over the years, the issues surrounding the division of zero by itself remained a mystery until year 2018 when the mystery was solved in numerous ways. Afterwards, the same solutions provided opened many other doors in academic space and one of the applications is in sure probabilities. This research is all about the sure probabilities computed from the zero divided by itself point of view. The solutions obtained in the computations are in harmony with logic and basic knowledge. A wide range of already existing probability distribution functions has been applied in different scenarios to compute the sure probabilities unanimously and new findings have also been encountered along the way. Some of the discrete and continuous probability distribution functions involved are the binomial, hypergeometric, negative binomial, Poisson, normal and exponential among others. It has been found in this work that sure probabilities can be evaluated from the division of zero by itself perspective. Another new finding is that in case of combinatorial, if the numerator is smaller than the denominator, then the solutions tend to zero when knowledge in gamma functions, integrations and factorials is applied. Again, if the case of continuous pdf involves integration and random variable specified in the direction of the parameter, then indirect computation of such probabilities should be applied. Finally, it has been found that the expansion of the domains of some of the parameters in some existing probability distribution functions can be considered and the restriction in conditional probabilities can be revised.

scholarly journals Reliability analysis of planar steel trusses based on p-box models

Vestnik MGSU ◽  
2021 ◽  
pp. 153-167
Author(s):  
Anastasia A. Soloveva ◽  
Sergey A. Solovev
Keyword(s):  
Probability Distribution ◽  
Reliability Analysis ◽  
Statistical Data ◽  
Random Variables ◽  
Random Variable ◽  
Distribution Functions ◽  
Structural Elements ◽  
Limit States ◽  
Load Model ◽  
Box Models

Introduction. The development of probabilistic approaches to the assessment of mechanical safety of bearing structural elements is one of the most relevant areas of research in the construction industry. In this research, probabilistic methods are developed to perform the reliability analysis of steel truss elements using the p-box (probability box) approach. This approach ensures a more conservative (interval-based) reliability assessment made within the framework of attaining practical objectives of the reliability analysis of planar trusses and their elements. The truss is analyzed as a provisional sequential mechanical system (in the language of the theory of reliability) consisting of elements that represent reliability values for each individual bar and truss node in terms of all criteria of limit states. Materials and methods. The co-authors suggest using p-blocks consisting of two boundary distribution functions designated for modeling random variables in the mathematical models of limit states performed within the framework of the truss reliability analysis instead of independent true functions of the probability distribution of random variables. Boundary distribution functions produce a probability distribution domain in which a true distribution function of a random variable is located. However this function is unknown in advance due to the aleatory and epistemic uncertainty. The choice of a p-block for modeling a random variable will depend on the type and amount of statistical information about the random variable. Results. The probabilistic snow load model and the numerical simulation of tests of steel samples of truss rods are employed to show that p-box models are optimal for modeling random variables to solve numerous practical problems of the probabilistic assessment of reliability of structural elements. The proposed p-box snow load model is based on the Gumbel distribution. The mathematical model used to perform the reliability analysis of planar steel truss elements is proposed. The co-authors provide calculation formulas to assess the reliability of a truss element for different types of p-blocks used to describe random variables depending on the amount of statistical data available. Conclusions. The application of statistically unsubstantiated hypotheses for choosing the probability distribution law or assessing the parameters of the probability distribution of a random variable leads to erroneous assessments of the reliability of structural elements, including trusses. P-boxes ensure a more careful reliability assessment of a structural element, but at the same time this assessment is less informative, as it is presented in the form of an interval. A more accurate reliability interval requires interval-based assessments of distribution parameters or types of p-boxes applied to mathematical models of the limit state, which entails an increase in the economic and labor costs of the statistical data.

scholarly journals Run Theory and Copula-Based Drought Risk Analysis for Songnen Grassland in Northeastern China

2019 ◽  
Vol 11 (21) ◽  
pp. 6032 ◽  
Author(s):  
Wu ◽  
Zhang ◽  
Bao ◽  
Guo
Keyword(s):  
Risk Analysis ◽  
Goodness Of Fit ◽  
Distribution Functions ◽  
Drought Severity ◽  
Dependence Structure ◽  
Drought Risk ◽  
Drought Event ◽  
Return Periods ◽  
Copula Functions ◽  
Run Theory

Droughts are among the more costly natural hazards, and drought risk analysis has become urgent for the proper planning and management of water resources in grassland ecosystems. We chose Songnen grassland as a case study, used a standardized precipitation evapotranspiration index (SPEI) to model drought characteristics, employed run theory to define the drought event, and chose copula functions to construct the joint distribution for drought variables. We applied two kinds of return periods to conduct a drought risk assessment. After evaluating and comparing several distribution functions, drought severity (DS) was best described by the generalized extreme value (GEV) distribution, whereas drought duration (DD) was best fitted by gamma distribution. The root mean square error (RMSE) and Akaike Information Criterion (AIC) goodness-of-fit measures to evaluate their performance, the best-performing copula is Frank copula to model the joint dependence structure for each drought variables. The results of the secondary return periods indicate that a higher risk of droughts occurs in Keshan county, Longjiang county, Qiqiha’er city, Taonan city, and Baicheng city. Furthermore, a relatively lower risk of drought was found in Bei’an city, Mingquan county, Qinggang county, and qian’an county, and also in the Changling county and Shuangliao city. According to the calculation of the secondary return periods, which considered all possible scenarios in our study, we found that the secondary return period may be the best indicator for evaluating grassland ecosystem drought risk management.

scholarly journals APPROXIMATING PROBABILITY DISTRIBUTION FUNCTIONS WITH FEW MOMENTS

2019 ◽  
Vol 50 (1) ◽  
pp. 21-25
Author(s):  
Emilio Wille
Keyword(s):  
Probability Distribution ◽  
Statistical Data ◽  
Piecewise Linear ◽  
Distribution Functions ◽  
Theoretical Simulation ◽  
Product Of Random Variables ◽  
Probability Distribution Functions ◽  
Piecewise Linear Approximations ◽  
Log Normal ◽  
Good Agreement

A procedure is presented for approximating a given probability distribution function or statistical data considering a subset of their moments.This is done by a method of fitting moments of a piecewise linear functionto the moments of the known data. The approach has many advantages over popular approximation approaches. The procedure is demonstrated with commonly used cdfs (Exponential, Gamma, Log-Normal, Normal) andmore difficult problems involving sum and product of random variables,obtaining good agreement between the theoretical/simulation curves and the piecewise linear approximations.

scholarly journals Frequency analysis of low flows in intermittent and non-intermittent rivers from hydrological basins in Turkey

2018 ◽  
Vol 19 (1) ◽  
pp. 30-39 ◽  
Author(s):  
Ebru Eris ◽  
Hafzullah Aksoy ◽  
Bihrat Onoz ◽  
Mahmut Cetin ◽  
Mehmet Ishak Yuce ◽  
...  
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Distribution Functions ◽  
Low Flow ◽  
Probability Distribution Functions ◽  
Low Flows ◽  
Intermittent Rivers ◽  
Log Normal ◽  
Best Fit

Abstract This study attempts to find out the best-fit probability distribution function to low flows using the up-to-date data of intermittent and non-intermittent rivers in four hydrological basins from different regions in Turkey. Frequency analysis of D = 1-, 7-, 14-, 30-, 90- and 273-day low flows calculated from the daily flow time series of each stream gauge was performed. Weibull (W2), Gamma (G2), Generalized Extreme Value (GEV) and Log-Normal (LN2) are selected among the 2-parameter probability distribution functions together with the Weibull (W3), Gamma (G3) and Log-Normal (LN3) from the 3-parameter probability distribution function family. Selected probability distribution functions are checked for their suitability to fit each D-day low flow sequence. LN3 mostly conforms to low flows by being the best-fit among the selected probability distribution functions in three out of four hydrological basins while W3 fits low flows in one basin. With the use of the best-fit probability distribution function, the low flow-duration-frequency curves are determined, which have the ability to provide the end-users with any D-day low flow discharge of any given return period.

scholarly journals Probability distribution functions of gas surface density in M 33

2018 ◽  
Vol 617 ◽  
pp. A125 ◽  
Author(s):  
Edvige Corbelli ◽  
Bruce G. Elmegreen ◽  
Jonathan Braine ◽  
David Thilker
Keyword(s):  
Star Formation ◽  
Probability Distribution ◽  
Power Law ◽  
Distribution Functions ◽  
Morphological Properties ◽  
Molecular Gas ◽  
Star Forming ◽  
Normal Functions ◽  
Probability Distribution Functions ◽  
Log Normal

Aims. We examine the interstellar medium (ISM) of M 33 to unveil fingerprints of self-gravitating gas clouds throughout the star-forming disk. Methods. The probability distribution functions (PDFs) for atomic, molecular, and total gas surface densities are determined at a resolution of about 50 pc over regions that share coherent morphological properties and considering cloud samples at different evolutionary stages in the star formation cycle. Results. Most of the total gas PDFs are well fit by log-normal functions whose width decreases radially outward. Because the HI velocity dispersion is approximately constant throughout the disk, the decrease in PDF width is consistent with a lower Mach number for the turbulent ISM at large galactocentric radii where a higher fraction of HI is in the warm phase. The atomic gas is found mostly at face-on column densities below NHlim = 2.5 × 1021 cm−2, with small radial variations of NHlim. The molecular gas PDFs do not show strong deviations from log-normal functions in the central region where molecular fractions are high. Here the high pressure and rate of star formation shapes the PDF as a log-normal function, dispersing self-gravitating complexes with intense feedback at all column densities that are spatially resolved. Power-law PDFs for the molecules are found near and above NHlim, in the southern spiral arm and in a continuous dense filament extending at larger galactocentric radii. In the filament nearly half of the molecular gas departs from a log-normal PDF, and power laws are also observed in pre-star-forming molecular complexes. The slope of the power law is between −1 and −2. This slope, combined with maps showing where the different parts of the power law PDFs come from, suggests a power-law stratification of the density within molecular cloud complexes, in agreement with the dominance of self-gravity.

scholarly journals EVALUATION OF THE BEST-FIT PROBABILITY OF DISTRIBUTION AND RETURN PERIODS OF RIVER DISCHARGE PEAKS. CASE STUDY: AWETU RIVER, JIMMA, ETHIOPIA

2019 ◽  
Vol 4 (4) ◽  
pp. 361-368 ◽  
Author(s):  
Tolera Abdisa Feyissa ◽  
Nasir Gebi Tukura
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Peak Discharge ◽  
Environmental Damage ◽  
Return Periods ◽  
Chi Squared ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Log Normal ◽  
Best Fit

The identification of the best distribution function is essential to estimate a river peak discharge or magnitude of river floods for management of watershed and ecosystems. However, inadequate estimation of the river peak discharge and floods magnitude may decrease the efficiency of water-resources management, resulting in soil erosion, landslides, environmental damage and ecosystem degradation. To overcome this problem in hydrology, different methods have been employed, applying a probability distribution.In this study to determine the suitable probability of distribution for estimating the annual discharge series with different return periods, the annual mean and peak discharges of the Awetu River (Jimma, Ethiopia) over a 24 years’ time period have been collected and used. After the homogeneity and consistency test, data were analyzed to predict extreme values and were applied in seven different probability distribution functions by using L-moment and easy fit methods. Then, three goodness of fit tests, Anderson-Darling (AD), Kolmogorov-Smirnov (KS), and Chi-Squared (x2) tests, were used to select the best probability distribution function for the study area. The obtained results indicate that, Log-normal distribution function is the best-fit distribution to estimate the peak discharge recurrence of the Awetu River. The 5-year, 10-year, 25-year, 50-year, 100-year and 1000-year return periods of discharge were calculated for this river. The results of this study are useful for the development of more accurate models of flooding inundation and hazard analysis. AVALIAÇÃO DA MELHOR PROBABILIDADE DE AJUSTE DE DISTRIBUIÇÃO E PERÍODOS DE RETORNO DOS PICOS DE DESCARGA FLUVIAL. ESTUDO DE CASO: AWETU RIVER, JIMMA, ETIÓPIAResumoAvaliação da melhor função de probabilidade de distribuição e de períodos de retorno de picos de descarga de rio. Estudo de caso: Rio Awetu, Jimma, Etiópia. A identificação da melhor função de distribuição é essencial para estimar um pico de descarga de rios ou a magnitude das inundações de bacias hidrográficas e ecossistemas, tendo em vista a gestão dos sistemas hídricos e dos ecossistemas. Entretanto, uma estimativa inadequada da magnitude do pico de vazão e inundações do rio pode diminuir a eficiência do gerenciamento dos recursos hídricos, resultando em erosão do solo, deslizamentos de terra, danos ambientais e degradação do ecossistema. Para superar esse problema na hidrologia, diferentes métodos foram empregados, aplicando funções de probabilidade de distribuição e retorno.Neste estudo, para determinar a probabilidade adequada de distribuição e para estimar séries de descarga anuais com diferentes períodos de retorno, foram usados dados de médias anuais de picos de descarga do Rio Awetu (Jimma, Etiópia) durante um período de 24 anos. Após o teste de homogeneidade e consistência, os dados foram analisados para prever valores extremos e foram aplicados a sete funções diferentes de probabilidade de distribuição, usando o momento L e métodos de ajuste fácil. Em seguida foram utilizados, três testes de qualidade de ajuste, Anderson-Darling (AD), Kolmogorov-Smirnov (KS), and Chi-Squared (x2), para selecionar a melhor função de probabilidade de distribuição para a área de estudo. Os resultados obtidos indicam que, a função de distribuição log-normal é a que mais se adequa para estimar a recorrência de picos de descarga do Rio Awetu. Os períodos de retorno de descarga de 5 anos, 10 anos, 25 anos, 50 anos, 100 anos e 1000 anos foram calculados para este rio. Os resultados deste estudo são úteis para o desenvolvimento de modelos mais precisos de inundação e análise de risco.Palavras-chave: Descarga de Rio. Qualidade de ajuste. Log Pearson Tipo III. Distribuição de probabilidade. 

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