scholarly journals Estimating Rainfall Design Values for the City of Oslo, Norway—Comparison of Methods and Quantification of Uncertainty

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1735 ◽  
Author(s):  
Julia Lutz ◽  
Lars Grinde ◽  
Anita Verpe Dyrrdal
Keyword(s):  
Bayesian Inference ◽  
Goodness Of Fit ◽  
Bayesian Method ◽  
Gumbel Distribution ◽  
Likelihood Estimation ◽  
Current Method ◽  
Credible Interval ◽  
Computational Method ◽  
Goodness Of Fit Tests ◽  
Idf Curves

Due to its location, its old sewage system, and the channelling of rivers, Oslo is highly exposed to urban flooding. Thus, it is crucial to provide relevant and reliable information on extreme precipitation in the planning and design of infrastructure. Intensity-Duration-Frequency (IDF) curves are a frequently used tool for that purpose. However, the computational method for IDF curves in Norway was established over 45 years ago, and has not been further developed since. In our study, we show that the current method of fitting a Gumbel distribution to the highest precipitation events is not able to reflect the return values for the long return periods. Instead, we introduce the fitting of a Generalised Extreme Value (GEV) distribution for annual maximum precipitation in two different ways, using (a) a modified Maximum Likelihood estimation and (b) Bayesian inference. The comparison of the two methods for 14 stations in and around Oslo reveals that the estimated median return values are very similar, but the Bayesian method provides upper credible interval boundaries that are considerably higher. Two different goodness-of-fit tests favour the Bayesian method; thus, we suggest using the Bayesian inference for estimating IDF curves for the Oslo area.

scholarly journals comparison of methods for the estimation of Weibull distribution parameters

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Felix Nwobi ◽  
Chukwudi Ugomma
Keyword(s):  
Weibull Distribution ◽  
Stock Prices ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Goodness Of Fit Tests ◽  
Distribution Parameters ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Maximum Likelihood Estimation Method

In this paper we study the different methods for estimation of the parameters of the Weibull distribution. These methods are compared in terms of their fits using the mean square error (MSE) and the Kolmogorov-Smirnov (KS) criteria to select the best method. Goodness-of-fit tests show that the Weibull distribution is a good fit to the squared returns series of weekly stock prices of Cornerstone Insurance PLC. Results show that the mean rank (MR) is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method (MLE) significantly outperformed other methods.

scholarly journals Selecting the best probability distribution for at-site flood frequency analysis; a study of Torne River

2019 ◽  
Vol 1 (12) ◽  
Author(s):  
Mahmood Ul Hassan ◽  
Omar Hayat ◽  
Zahra Noreen
Keyword(s):  
Probability Distribution ◽  
Frequency Analysis ◽  
Goodness Of Fit ◽  
Direct Method ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Goodness Of Fit Tests ◽  
Pearson Type

AbstractAt-site flood frequency analysis is a direct method of estimation of flood frequency at a particular site. The appropriate selection of probability distribution and a parameter estimation method are important for at-site flood frequency analysis. Generalized extreme value, three-parameter log-normal, generalized logistic, Pearson type-III and Gumbel distributions have been considered to describe the annual maximum steam flow at five gauging sites of Torne River in Sweden. To estimate the parameters of distributions, maximum likelihood estimation and L-moments methods are used. The performance of these distributions is assessed based on goodness-of-fit tests and accuracy measures. At most sites, the best-fitted distributions are with LM estimation method. Finally, the most suitable distribution at each site is used to predict the maximum flood magnitude for different return periods.

scholarly journals Modified generalized marshall-olkin family of distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 18
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Goodness Of Fit Tests ◽  
New Family ◽  
Family Of Distributions

In this article, we propose a new family of distributions using the T-X family named as modified generalized Marshall-Olkin family of distributions. Comprehensive mathematical and statistical properties of this family of distributions are provided. The model parameters are estimated by maximum likelihood method. The maximum likelihood estimation under Type-II censoring is also discussed. Two lifetime data sets are used to show the suitability and applicability of the new family of distributions. For comparison purposes, different goodness of fit tests are used.  

scholarly journals Goodness of Fit Tests for the Log-Logistic Distribution Based on Cumulative Entropy under Progressive Type II Censoring

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 361 ◽  
Author(s):  
Yuge Du ◽  
Wenhao Gui
Keyword(s):  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Logistic Distribution ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Goodness Of Fit Tests ◽  
Progressive Type ◽  
Leibler Information ◽  
Cumulative Residual ◽  
Progressive Type Ii Censoring

In this paper, we propose two new methods to perform goodness-of-fit tests on the log-logistic distribution under progressive Type II censoring based on the cumulative residual Kullback-Leibler information and cumulative Kullback-Leibler information. Maximum likelihood estimation and the EM algorithm are used for statistical inference of the unknown parameter. The Monte Carlo simulation is conducted to study the power analysis on the alternative distributions of the hazard function monotonically increasing and decreasing. Finally, we present illustrative examples to show the applicability of the proposed methods.

scholarly journals Development of a General Equation for Intensity-Duration-Frequency (IDF): Iraq

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Hasan Mahdi
Keyword(s):  
Water Resource Management ◽  
Goodness Of Fit ◽  
Flash Flood ◽  
Repeated Cycle ◽  
Goodness Of Fit Tests ◽  
Pearson Type ◽  
Chi Squared ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
Anderson Darling

In the field of water resource management, rainfall intensity-duration-frequency (IDF) curves are of great importance, especially in the design of hydraulic structures and the assessment of flash-flood risks. The aim of this study is to obtain IDF curves and find empirical equations for rain duration for Al-Najaf city in the southwest of Iraq. Rainfall data for 30 years, from 1989 to 2018, were collected. The practical reduction equation of the Indian Meteorological Department (IMD), with six methods of probability distribution, was used for short intervals (0.25, 0.5, 1, 2, 3, 6, 12, and 24 hours) with a specified recurrence period (100, 50, 25, 10, 5, and 2 years). The Kolmogorov-Smirnov, chi-squared, and Anderson-Darling goodness of fit tests were used with the help of EasyFit 5.6 software. The findings revealed that the highest intensity of rainfall occurs during a repeated cycle of 100 years with a duration of 0.25 hours, while the lowest intensity of rainfall occurs during a repeated cycle of 2 years with a duration of 24 hours. In the results obtained from the six methods, as well as the superiority of the log Pearson type III method, the consistency of the fit tests showed some convergence.

scholarly journals ASSESSMENT OF THE BEST PROBABILITY DISTRIBUTION METHOD IN RAINFALL FREQUENCY ANALYSIS FOR A TROPICAL REGION

2021 ◽  
Vol 33 (1) ◽  
Author(s):  
Stephen Luo Sheng Yong ◽  
Jing Lin Ng ◽  
Yuk Feng Huang ◽  
Chun Kit Ang
Keyword(s):  
Goodness Of Fit ◽  
Gumbel Distribution ◽  
Tropical Region ◽  
Distribution Method ◽  
Maximum Rainfall ◽  
Significance Level ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Passing Rate ◽  
Pearson Type

The Intensity-Duration-Frequency (IDF) curve defines the relationship between rainfall intensities at certain durations and with the frequencies. The IDF Curve is extensively used in many applications such as flood modelling and peak discharge estimation. Over the years, the frequent occurrence of flood has become a great challenge in Kelantan river basin. Herein, IDF curves using frequency analyses based on different distributions were developed and compared. The historical rainfall data at eight rainfall stations for the period of 1985-2019 were selected for the assessment purpose. The Gumbel, Normal and Log Pearson Type III distributions were fitted into the annual maximum rainfall series for durations varying from 30 minutes to 24 hours. The goodness of fit tests were then used to evaluate the performances of each frequency distribution. It was found that the Gumbel distribution gave the highest passing rate followed by the Log Pearson Type III and then the Normal distributions. The Gumbel distribution resulted in respective 86% and 75% passing rate since most of the p-values generated by both the K-S and the Mann-Whitney test were greater than 5% of significance level leading to the acceptance of the null hypothesis. Thus, the Gumbel distribution is suggested for the frequency analyses in this study.

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