Establishment of a Stochastic Model for Sustainable Economic Flood Management in Yewa Sub-Basin, Southwest Nigeria

Of all natural disasters, floods have been considered to have the greatest potential damage. The magnitude of economic damages and number of people affected by flooding have recently increased globally due to climate change. This study was based on the establishment of a stochastic model for reducing economic floods risk in Yewa sub-basin, by fitting maximum annual instantaneous discharge into four probability distributions. Daily discharge of River Yewa gauged at Ijaka-Oke was used to establish a rating curve for the sub-basin, while return periods of instantaneous peak floods were computed using the Hazen plotting position. Flood magnitudes were found to increase with return periods based on Hazen plotting position. In order to ascertain the most suitable probability distribution for predicting design floods, the performance evaluation of the models using root mean square error was employed. In addition, the four probability models were subjected to goodness of fit test besed on Anderson-Darling (A2) and Kolmogorov-Smirnov (KS). As a result of the diagnostics test the Weibul probability distribution was confirmed to fit well with the empirical data of the study area. The stochastic model generated from the Weibul probability distribution, could be used to enhance sustainable development by reducing economic flood damages in the sub-basin.

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Analysis of Magnitude and Frequency of Floods in the Damanganga Basin: Western India

Hydrospatial Analysis ◽

10.21523/gcj3.2021050101 ◽

2021 ◽

Vol 5 (1) ◽

pp. 1-11

Author(s):

Vitthal Anwat ◽

Pramodkumar Hire ◽

Uttam Pawar ◽

Rajendra Gunjal

Keyword(s):

Probability Distribution ◽

Probability Distributions ◽

Flood Frequency ◽

Flood Frequency Analysis ◽

Western India ◽

Type I ◽

Return Periods ◽

Pearson Type ◽

Kolmogorov Smirnov ◽

Anderson Darling

Flood Frequency Analysis (FFA) method was introduced by Fuller in 1914 to understand the magnitude and frequency of floods. The present study is carried out using the two most widely accepted probability distributions for FFA in the world namely, Gumbel Extreme Value type I (GEVI) and Log Pearson type III (LP-III). The Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) methods were used to select the most suitable probability distribution at sites in the Damanganga Basin. Moreover, discharges were estimated for various return periods using GEVI and LP-III. The recurrence interval of the largest peak flood on record (Qmax) is 107 years (at Nanipalsan) and 146 years (at Ozarkhed) as per LP-III. Flood Frequency Curves (FFC) specifies that LP-III is the best-fitted probability distribution for FFA of the Damanganga Basin. Therefore, estimated discharges and return periods by LP-III probability distribution are more reliable and can be used for designing hydraulic structures.

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Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

Journal of Mathematics and Statistics Studies ◽

10.32996/jmss.2021.2.2.7 ◽

2021 ◽

Vol 2 (2) ◽

pp. 60-67

Author(s):

Rashidul Hasan Rashidul Hasan

Keyword(s):

Probability Distribution ◽

Goodness Of Fit ◽

Probability Distributions ◽

Probability Model ◽

Temperature Data ◽

Maximum Temperature ◽

Chi Square ◽

Goodness Of Fit Tests ◽

Anderson Darling ◽

Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

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A comparison of three parameter estimation methods of the gamma distribution of annual maximum low flow duration and deficit in the Upper Vistula catchment (Poland)

ITM Web of Conferences ◽

10.1051/itmconf/20182300001 ◽

2018 ◽

Vol 23 ◽

pp. 00001

Author(s):

Katarzyna Baran-Gurgul

Keyword(s):

Gamma Distribution ◽

Goodness Of Fit ◽

Probability Distributions ◽

Low Flow ◽

Estimation Methods ◽

Goodness Of Fit Test ◽

Flow Duration ◽

Distribution Parameters ◽

Anderson Darling ◽

Parameter Estimation Methods

Based on 30-year 24-hour flow sequences at 69 water gauging stations in the Upper Vistula catchment, it was determined that the probability distributions of the low flow duration and its maximum annual deficit can be described by the gamma distribution with the estimated parameters by the methods: MOM, the method of moments, LMOM, the method of linear moments, and MLE, the method of maximum likelihood. The stationarity of the time series was tested by the Mann-Kendall correlation using the Hamed and Rao variance correction. The low flows were defined by the SPA method, with the limit flow Q70%. The quality of the match was tested by the Anderson-Darling goodness of fit test. This test allowed accepting the gamma distribution in all analysed cases, regardless of the method used to estimate the distribution parameters, since the pv (p-values) values were greater than 5% (over 18% for Tmax and 7.5% for Vmax). The highest pv values for individual water gauging stations, as well as the highest 90% Tmax and Vmax quantiles were noted using LMOM to estimate the gamma distribution parameters. The highest 90% Tmax and Vmax quantiles were observed in the uppermost part of the studied area.

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Probability Distribution of Rainfall in Medan

Journal of Research in Mathematics Trends and Technology ◽

10.32734/jormtt.v1i2.2835 ◽

2019 ◽

Vol 1 (2) ◽

pp. 43-49 ◽

Cited By ~ 1

Author(s):

Elly Rosmaini

Keyword(s):

Probability Distribution ◽

Gamma Distribution ◽

Goodness Of Fit ◽

Monthly Rainfall ◽

Rainfall Data ◽

Goodness Of Fit Test ◽

Normal Distributions ◽

Lognormal Distributions ◽

Kolmogorov Smirnov ◽

Anderson Darling

In this paper we chose three stations in Medan City , Indonesia to estimate Monthly Rainfall Data i.e. Tuntungan, Tanjung Selamat, and Medan Selayang Stations. We took the data from 2007 to 2016. In this case fitted with Normal, Gamma, and Lognormal Distributions. To estimate parameters, we used this method. Furthermore, Kolmogorov-Smirnov and Anderson Darling tests were used the goodness-of-fit test. The Gamma and Normal Distributions is suitable for Tuntungan and Medan Selayang Stations were stated by Kolmogorov-Smirnov's test. Anderson Darling's test stated that Gamma Distribution was suitable for all stations.

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Probability distributions for explaining hydrological losses in South Australian catchments

Hydrology and Earth System Sciences ◽

10.5194/hess-17-4541-2013 ◽

2013 ◽

Vol 17 (11) ◽

pp. 4541-4553 ◽

Cited By ~ 5

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.

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A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan

Open Life Sciences ◽

10.1515/biol-2016-0057 ◽

2016 ◽

Vol 11 (1) ◽

pp. 432-440 ◽

Cited By ~ 10

Author(s):

M. T. Amin ◽

M. Rizwan ◽

A. A. Alazba

Keyword(s):

Probability Distribution ◽

Goodness Of Fit ◽

Probability Distributions ◽

Future Research ◽

Maximum Rainfall ◽

Type Iii ◽

Goodness Of Fit Tests ◽

Pearson Type ◽

Northern Regions ◽

Best Fit

AbstractThis study was designed to find the best-fit probability distribution of annual maximum rainfall based on a twenty-four-hour sample in the northern regions of Pakistan using four probability distributions: normal, log-normal, log-Pearson type-III and Gumbel max. Based on the scores of goodness of fit tests, the normal distribution was found to be the best-fit probability distribution at the Mardan rainfall gauging station. The log-Pearson type-III distribution was found to be the best-fit probability distribution at the rest of the rainfall gauging stations. The maximum values of expected rainfall were calculated using the best-fit probability distributions and can be used by design engineers in future research.

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Bivariate Hydrologic Risk Assessment of Flood Episodes using the Notation of Failure Probability

Civil Engineering Journal ◽

10.28991/cej-2020-03091599 ◽

2020 ◽

Vol 6 (10) ◽

pp. 2002-2023

Author(s):

Shahid Latif ◽

Firuza Mustafa

Keyword(s):

Failure Probability ◽

Goodness Of Fit ◽

Peak Flow ◽

Gaussian Copula ◽

Dependence Structure ◽

Distribution Analysis ◽

Return Periods ◽

Goodness Of Fit Test ◽

Flood Peak ◽

Flood Volume

Floods are becoming the most severe and challenging hydrologic issue at the Kelantan River basin in Malaysia. Flood episodes are usually thoroughly characterized by flood peak discharge flow, volume and duration series. This study incorporated the copula-based methodology in deriving the joint distribution analysis of the annual flood characteristics and the failure probability for assessing the bivariate hydrologic risk. Both the Archimedean and Gaussian copula family were introduced and tested as possible candidate functions. The copula dependence parameters are estimated using the method-of-moment estimation procedure. The Gaussian copula was recognized as the best-fitted distribution for capturing the dependence structure of the flood peak-volume and peak-duration pairs based on goodness-of-fit test statistics and was further employed to derive the joint return periods. The bivariate hydrologic risks of flood peak flow and volume pair, and flood peak flow and duration pair in different return periods (i.e., 5, 10, 20, 50 and 100 years) were estimated and revealed that the risk statistics incrementally increase in the service lifetime and, at the same instant, incrementally decrease in return periods. In addition, we found that ignoring the mutual dependency can underestimate the failure probabilities where the univariate events produced a lower failure probability than the bivariate events. Similarly, the variations in bivariate hydrologic risk with the changes of flood peak in the different synthetic flood volume and duration series (i.e., 5, 10, 20, 50 and 100 years return periods) under different service lifetimes are demonstrated. Investigation revealed that the value of bivariate hydrologic risk statistics incrementally increases over the project lifetime (i.e., 30, 50, and 100 years) service time, and at the same time, it incrementally decreases in the return period of flood volume and duration. Overall, this study could provide a basis for making an appropriate flood defence plan and long-lasting infrastructure designs. Doi: 10.28991/cej-2020-03091599 Full Text: PDF

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Statistical characteristics for the defect occurrence of raw silk

Textile Research Journal ◽

10.1177/0040517519865040 ◽

2019 ◽

Vol 90 (3-4) ◽

pp. 302-312

Author(s):

Jian-mei Xu ◽

Ying Zhou ◽

Jiantao Niu ◽

Dongping Wu ◽

Lun Bai

Keyword(s):

Goodness Of Fit ◽

Probability Distributions ◽

Capacitive Sensor ◽

Test Method ◽

International Organization ◽

Statistical Characteristics ◽

Goodness Of Fit Test ◽

Polya Distribution ◽

Silk Filament ◽

Better Than

In order to consider different defects that occur during the computer simulation of raw silk size series, it is necessary to find out the statistical characteristics for the defect occurrence of raw silk. Under the newest International Organization for Standardization standard for electronic testing of raw silk, the defects are classified into small slubs, big slubs, thick places, thin places, and small imperfection elements. By analyzing some probability distributions that happen during the silk reeling process and the formation of the defects, the study proposed that Pólya distribution may fit better than Poisson distribution in describing the number of defects formed in a certain length of silk filament. To verify this theoretical deduction experimentally, the defects for 15 lots of raw silk were tested every 1000 meters using an electronic tester for raw silk; each time 12 skeins were tested together and each test was repeated from 13 to 17 times. A goodness-of-fit test method for Poisson and Pólya distributions was deduced, which was used to analyze the statistical characteristics for the defects except for small imperfection elements. The results showed that when using the capacitive sensor, the defects of big slubs, small slubs, and thick places had a Pólya distribution with a weak spreading characteristic; the thin places were a combination of independent Pólya distributions, and each subclass of thin places took Pólya distribution; when using the optical sensor, all the defects had a Pólya distribution, which was in line with the theoretical deduction.

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Estimation of flood frequency using statistical method: Mahanadi River basin, India

H2Open Journal ◽

10.2166/h2oj.2020.004 ◽

2020 ◽

Vol 3 (1) ◽

pp. 189-207

Author(s):

Sandeep Samantaray ◽

Abinash Sahoo

Keyword(s):

Stream Flow ◽

Goodness Of Fit ◽

Central India ◽

Extreme Value ◽

Flood Frequency ◽

Goodness Of Fit Test ◽

Mahanadi River ◽

Goodness Of Fit Tests ◽

Study Results ◽

Anderson Darling

Abstract Estimating stream flow has a substantial financial influence, because this can be of assistance in water resources management and provides safety from scarcity of water and conceivable flood destruction. Four common statistical methods, namely, Normal, Gumbel max, Log-Pearson III (LP III), and Gen. extreme value method are employed for 10, 20, 30, 35, 40, 50, 60, 70, 75, 100, 150 years to forecast stream flow. Monthly flow data from four stations on Mahanadi River, in Eastern Central India, namely, Rampur, Sundargarh, Jondhra, and Basantpur, are used in the study. Results show that Gumbel max gives better flow discharge value than the Normal, LP III, and Gen. extreme value methods for all four gauge stations. Estimated flood values for Rampur, Sundargarh, Jondhra, and Basantpur stations are 372.361 m3/sec, 530.415 m3/sec, 2,133.888 m3/sec, and 3,836.22 m3/sec, respectively, considering Gumbel max. Goodness-of-fit tests for four statistical distribution techniques applied in the present study are also evaluated using Kolmogorov–Smirov, Anderson–Darling, Chi-squared tests at critical value 0.05 for the four proposed gauge stations. Goodness-of-fit test results show that Gen. extreme value gives best results at Rampur, Sundergarh, and Jondhra gauge stations followed by LP III, whereas LP III is the best fit for Basantpur, followed by Gen. extreme value.

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The Effect of Sample Size on Bivariate Rainfall Frequency Analysis of Extreme Precipitation

Proceedings ◽

10.3390/ecws-3-05815 ◽

2018 ◽

Vol 7 (1) ◽

pp. 19 ◽

Cited By ~ 1

Author(s):

Nikoletta Stamatatou ◽

Lampros Vasiliades ◽

Athanasios Loukas

Keyword(s):

Sample Size ◽

Frequency Analysis ◽

Extreme Precipitation ◽

Goodness Of Fit ◽

Return Periods ◽

Goodness Of Fit Test ◽

Maximum Rainfall ◽

Rainfall Frequency ◽

Rainfall Frequency Analysis ◽

Pseudo Likelihood Estimation

The objective of this study is to compare univariate and joint bivariate return periods of extreme precipitation that all rely on different probability concepts in selected meteorological stations in Cyprus. Pairs of maximum rainfall depths with corresponding durations are estimated and compared using annual maximum series (AMS) for the complete period of the analysis and 30-year subsets for selected data periods. Marginal distributions of extreme precipitation are examined and used for the estimation of typical design periods. The dependence between extreme rainfall and duration is then assessed by an exploratory data analysis using K-plots and Chi-plots and the consistency of their relationship is quantified by Kendall’s correlation coefficient. Copulas from Archimedean, Elliptical, and Extreme Value families are fitted using a pseudo-likelihood estimation method, evaluated according to the corrected Akaike Information Criterion and verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic. The selected copula functions and the corresponding conditional and joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results highlight the effect of sample size on univariate and bivariate rainfall frequency analysis for hydraulic engineering design practices.

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