scholarly journals Probability distributions for explaining hydrological losses in South Australian catchments

2013 ◽  
Vol 10 (4) ◽  
pp. 4597-4626
Author(s):  
S. H. P. W. Gamage ◽  
G. A. Hewa ◽  
S. Beecham
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Joint Probability ◽  
Accurate Estimation ◽  
Rainfall Runoff ◽  
Design Flood ◽  
Wide Variability ◽  
Multiple Variables ◽  
Two Parameter ◽  
Non Parametric

Abstract. The wide variability of hydrological losses in catchments is due to multiple variables that affect the rainfall-runoff process. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall-runoff models. Using representative single values of losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. Probability distributions can be used as a better representation of losses. In particular, using joint probability approaches (JPA), probability distributions can be incorporated into hydrological loss parameters in design models. However, lack of understanding of loss distributions limits the benefit of using JPA. The aim of this paper is to identify a probability distribution function that can successfully describe hydrological losses in South Australian (SA) catchments. This paper describes suitable parametric and non-parametric distributions that can successfully describe observed loss data. The goodness-of-fit of the fitted distributions and quantification of the errors associated with quantile estimation are also discussed a two-parameter Gamma distribution was identified as one that successfully described initial loss (IL) data of the selected catchments. Also, a non-parametric standardised distribution of losses that describes both IL and continuing loss (CL) data were identified. The results obtained for the non-parametric methods were compared with similar studies carried out in other parts of Australia and a remarkable degree of consistency was observed. The results will be helpful in improving design flood applications.

scholarly journals Probability distributions for explaining hydrological losses in South Australian catchments

2013 ◽  
Vol 17 (11) ◽  
pp. 4541-4553 ◽  
Author(s):  
S. H. P. W. Gamage ◽  
G. A. Hewa ◽  
S. Beecham
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Rainfall Runoff ◽  
Distribution Fitting ◽  
Distribution Method ◽  
Wide Variability ◽  
Anderson Darling

Abstract. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall–runoff models. The use of representative single values of hydrological losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. The probability distribution method is potentially a better technique to describe losses. However, a lack of understanding of how losses are distributed can limit the use of this technique. This paper aims to identify a probability distribution function that can successfully describe hydrological losses of a catchment of interest. The paper explains the systematic process of identifying probability distribution functions, the problems faced during the distribution fitting process and a new generalised method to test the adequacy of fitted distributions. The goodness-of-fit of the fitted distributions are examined using the Anderson–Darling test and the Q–Q plot method and the errors associated with quantile estimation are quantified by estimating the bias and mean square error (MSE). A two-parameter gamma distribution was identified as one that successfully describes initial loss (IL) data for the selected catchments. Further, non-parametric standardised distributions that describe both IL and continuing loss data are also identified. This paper will provide a significant contribution to the Australian Rainfall and Runoff (ARR) guidelines that are currently being updated, by improving understanding of hydrological losses in South Australian catchments. More importantly, this study provides new knowledge on how IL in a catchment is characterised.

The joint probability distribution function of structure factors with rational indices. IV. The P1 case

1999 ◽  
Vol 55 (3) ◽  
pp. 512-524
Author(s):  
Carmelo Giacovazzo ◽  
Dritan Siliqi ◽  
Cristina Fernández-Castaño
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Joint Probability ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Joint Probability Distribution ◽  
Structure Factors ◽  
Joint Probability Distributions ◽  
The Hilbert Transform

The method of the joint probability distribution functions of structure factors has been extended to reflections with rational indices. The most general case, space group P1, has been considered. The positional parameters are the primitive random variables of our probabilistic approach, while the reflection indices are kept fixed. Quite general joint probability distributions have been considered from which conditional distributions have been derived: these proved applicable to the accurate estimation of the real and imaginary parts of a structure factor, given prior information on other structure factors. The method is also discussed in relation to the Hilbert-transform techniques.

scholarly journals Effects of Probability-Distributed Losses on Flood Estimates Using Event-Based Rainfall-Runoff Models

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2049
Author(s):  
Melanie Loveridge ◽  
Ataur Rahman
Keyword(s):  
Probability Distributions ◽  
Data Sets ◽  
Rainfall Runoff ◽  
Design Flood ◽  
Ungauged Catchments ◽  
Large Dataset ◽  
Loss Data ◽  
Flood Estimation ◽  
Historic Data ◽  
Event Based

Probability distributions of initial losses are investigated using a large dataset of catchments throughout Australia. The variability in design flood estimates caused by probability-distributed initial losses and associated uncertainties are investigated. Based on historic data sets in Australia, the Gamma and Beta distributions are found to be suitable for describing initial loss data. It has also been found that the central tendency of probability-distributed initial loss is more important in design flood estimation than the form of the probability density function. Findings from this study have notable implications on the regionalization of initial loss data, which is required for the application of Monte Carlo methods for design flood estimation in ungauged catchments.

scholarly journals Probability Distribution for the Visually Observed Fractional Cloud Cover over the Ocean

2018 ◽  
Vol 31 (8) ◽  
pp. 3207-3232 ◽  
Author(s):  
Marina Aleksandrova ◽  
Sergey K. Gulev ◽  
Konstantin Belyaev
Keyword(s):  
Probability Distribution ◽  
Cloud Cover ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
World Ocean ◽  
Accurate Estimation ◽  
Fractional Cloud ◽  
Low Cloud ◽  
Different Shapes ◽  
Low Cloud Cover

Abstract The authors suggest a three-parameter bounded distribution from the family of mixed gamma distributions for characterizing the probability density distributions of fractional total and low cloud cover over the global oceans. The authors derive both the continuous form of this distribution and its discrete counterpart, which can be directly applied to cloud cover reports. The distribution is applied to the cloud cover characteristics reported by voluntary observing ships (VOS) for the period from 1950 to 2011 after filtering nighttime observations with poor lunar illumination. The suggested distribution demonstrates a high goodness of fit to the data and good skill in capturing probability distributions with different shapes. The authors present seasonal climatologies of the parameters of the derived distribution for the chosen 60-yr period and demonstrate that applying the PDF-based concept to the analysis of cloud cover allows identification of areas where similar mean cloud amounts can be produced by probability distributions with very different shapes. The roles of the different parameters of the distribution in producing the observed cloud conditions in different regions of the World Ocean are discussed. The application of the derived probability distribution allows for accurate estimation of the percentiles of the distribution, which represent the probabilities of specific cloud conditions. These probabilities are presented for both total and low cloud cover, as well as for daytime and nighttime. The authors also discuss the applicability of the suggested distribution for the validation of different cloud cover data products over the globe and the prospects of additional applications.

scholarly journals Evaluation of Various Probability Distributions for Deriving Design Flood Featuring Right-Tail Events in Pakistan

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1603 ◽  
Author(s):  
Muhammad Rizwan ◽  
Shenglian Guo ◽  
Feng Xiong ◽  
Jiabo Yin
Keyword(s):  
Water Resource Management ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Synthetic Data ◽  
Structure Design ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Data Series ◽  
Design Flood ◽  
Goodness Of Fit Test

Design flood estimation is very important for hydraulic structure design, reservoir operation, and water resources management. During the last few decades, severe flash floods have caused substantial human, agricultural, and economic damages in Pakistan during the Monsoon seasons. However, despite phenomenal losses, the flood characteristics are rarely investigated. In this paper, flood frequency analysis (FFA) on four major rivers over Pakistan is performed to probe probability distributions (PDs)at the right-tail flood events. For this purpose, (i) we employed ten different probability distributions associating with an L-moments method for constructing FFA models across Pakistan; (ii) we evaluated the best-fit distribution by using goodness-of-fit test and statistical criteria; and finally; (iii) we devised a Monte Carlo simulation to systematically evaluate the robustness of a selected distribution’s fitting performance by using a synthetic data series of different sizes. Our results indicated that generalized Pareto and Weibull emerged as the most viable options for quantifying hydrological quantiles for most of the river basins in Pakistan. Our main findings would provide rich information as references for flood risk assessment and water resource management in Pakistan.

scholarly journals Evaluation of design flood estimates – a case study for Norway

2017 ◽  
Vol 49 (2) ◽  
pp. 450-465 ◽  
Author(s):  
Florian Kobierska ◽  
Kolbjørn Engeland ◽  
Thordis Thorarinsdottir
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Estimation Method ◽  
Predictive Performance ◽  
Design Flood ◽  
Record Length ◽  
Moments Method ◽  
Initial Hypothesis ◽  
Original Record ◽  
Predictive Fit

Abstract The aim of this study was to evaluate the predictive fit of probability distributions to annual maximum flood data, and in particular to evaluate (1) which combination of distribution and estimation method gives the best fit and (2) whether the answer to (1) depends on record length. These aims were achieved by assessing the sensitivity to record length of the predictive performance of several probability distributions. A bootstrapping approach was used by resampling (with replacement) record lengths of 30 to 90 years (50 resamples for each record length) from the original record and fitting distributions to these subsamples. Subsequently, the fits were evaluated according to several goodness-of-fit measures and to the variability of the predicted flood quantiles. Our initial hypothesis that shorter records favor two-parameter distributions was not clearly supported. The ordinary moments method was the most stable while providing equivalent goodness-of-fit.

Property Rights Freedom and Innovation: Eponymous Skills in Women's Gymnastics

2021 ◽  
pp. 152700252110558
Author(s):  
Franklin G. Mixon ◽  
Richard J. Cebula
Keyword(s):  
Soviet Union ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Joint Probability ◽  
Soviet Bloc ◽  
Frequency Distributions ◽  
Goodness Of Fit Tests ◽  
The Soviet Union ◽  
Joint Probability Distributions ◽  
The Impact

Prior research uses the collapse of Soviet-style communism in 1991 as a de facto experimental framework within which to examine the impact of prospective benefits on the motivation of athletes to succeed in the Olympic Games. Prior to the collapse, successful Soviet Bloc Olympians were provided extraordinary living conditions and lifestyles. These rewards evaporated with the demise of the Soviet Union in 1991, subsequently resulting in relatively poorer Olympic performances of Soviet Bloc athletes. The current study extends earlier work by investigating the impact of appropriability on the supply of innovation by examining the frequency of eponymous skills in women's gymnastics before and during the transition to a new market-based economic order. Our central hypothesis is that following the dissolution the communist governments of the Soviet Bloc and its satellites, the supply of innovation in the form of eponymous skills in women's gymnastics from these countries has fallen. Frequency distributions of eponymous skills in women's gymnastics both prior to and after the dissolution of the aforementioned communist regimes support this hypothesis, as do results from goodness-of-fit tests and stochastic dominance analysis of joint probability distributions.

scholarly journals Deriving Design Flood Hydrographs Based on Copula Function: A Case Study in Pakistan

Water ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1531 ◽  
Author(s):  
Muhammad Rizwan ◽  
Shenglian Guo ◽  
Jiabo Yin ◽  
Feng Xiong
Keyword(s):  
Probability Distributions ◽  
Joint Probability ◽  
Copula Function ◽  
Indus Basin ◽  
Design Flood ◽  
Design Standards ◽  
Flood Peak ◽  
Combination Methods ◽  
Environmental Recovery ◽  
Basin System

Flood events are characterized by flood peaks and volumes that can be mutually constructed using a copula function. The Indus basin system of Pakistan is periodically threatened by floods during monsoon seasons and thus causes huge losses to infrastructure as well as the community and economy. The design flood hydrograph (DFH) of suitable magnitude and degree is imperative for sheltering dams against the flood risk. The hydrological pair of flood peak and volume is required to be defined using a multivariate analysis method. In this paper, the joint probability function of the hydrological pair is employed to derive the DFH in the Indus basin system of Pakistan. Firstly, we compared the fitting performance of different probability distributions (PDs) as a marginal distribution. Next, we compared the Archimedean family of copulas to construct the bivariate joint distribution of flood peak and volume. Later, the equal frequency combination (EFC) method and most likely combination (MLC) method using “OR” joint return period (JRPor), was involved to derive the design flood quantiles. Finally, we derived the DFH using the two combination methods based on Gumbel–Hougaard copula for different return periods. We presented the combination methods for updating the shape of the DFH in Pakistan. Our study will contribute towards the improvement of design standards of dams and environmental recovery in Pakistan.

LABORATORY TESTS OF THYROID FUNCTION IN HYPERTHYROIDISM II.

1969 ◽  
Vol 62 (4_Suppla) ◽  
pp. S23-S35
Author(s):  
B.-A. Lamberg ◽  
O. P. Heinonen ◽  
K. Liewendahl ◽  
G. Kvist ◽  
M. Viherkoski ◽  
...  
Keyword(s):  
Thyroid Function ◽  
Laboratory Tests ◽  
Goodness Of Fit ◽  
Point Of View ◽  
Accurate Estimation ◽  
Diagnostic Efficiency ◽  
Normal Limits ◽  
Significant Difference ◽  
Crossing Point ◽  
Hyperthyroid Patients

ABSTRACT The distributions of 13 variables based on 10 laboratory tests measuring thyroid function were studied in euthyroid controls and in patients with toxic diffuse or toxic multinodular goitre. Density functions were fitted to the empirical data and the goodness of fit was evaluated by the use of the χ2-test. In a few instances there was a significant difference but the material available was in some respects too small to allow a very accurate estimation. The normal limits for each variable was defined by the 2.5 and 97.5 percentiles. It appears that in some instances these limits are too rigorous from the practical point of view. It is emphasized that the crossing point of the functions for euthyroid controls and hyperthyroid patients may be a better limit to use. In a preliminary analysis of the diagnostic efficiency the variables of total or free hormone concentration in the blood proved clearily superior to all other variables.

A Study on Rainfall-Runoff Frequency Analysis for Estimating Design Flood

2015 ◽  
Vol 48 (8) ◽  
pp. 605-612 ◽  
Author(s):  
Choi Jongin ◽  
◽  
Ji Jungwon ◽  
Yi Jaeeung
Keyword(s):  
Frequency Analysis ◽  
Rainfall Runoff ◽  
Design Flood
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