scholarly journals Comparison of Generalized Extreme Value, Log Normal and Weibull Distributions for Assessment of Low-Flow

2021 ◽  
Vol 11 ◽  
pp. 34-41
Author(s):  
N. Vivekanandan
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Probability Distributions ◽  
Water Quality Management ◽  
Extreme Value ◽  
Qualitative Assessment ◽  
Low Flow ◽  
Likelihood Method ◽  
Generalized Extreme Value ◽  
Log Normal

Assessment of low-flow is an important aspect for water quality management, reservoir storage design, determining minimum release policy and safe surface water withdrawals. For which, the annual minimum d-day average flow is generally adopted procedure for characterizing the low-flow in a stream, which can be obtained by averaging the flow using moving average method for ‘d’ consecutive days viz., 7-, 10-, 14- and 30- days. This paper presents a study on comparison of three probability distributions such as Generalized Extreme Value, 2-parameter Log Normal (LN2) and Weibull adopted in estimation of low-flow for river Cauvery at Kollegal gauging site. The parameters are determined by three methods viz., method of moments, maximum likelihood method and L-Moments (LMO), and are used for estimation of low-flow. The adequacy of fitting probability distributions adopted in low-flow frequency analysis is evaluated by quantitative assessment through Goodness-of-Fit (viz., Chi-Square and Kolmogorov-Smirnov) and diagnostic (viz., correlation coefficient and root mean squared error) tests, and qualitative assessment using the fitted curves of the estimated low-flow. The results of quantitative and qualitative assessments indicate that LN2 (LMO) is better suited amongst three distributions adopted in estimation of 7-, 10-, 14- and 30- day low-flows for river Cauvery at Kollegal site.

scholarly journals Intercomparison of estimators of extreme value family of distributions for rainfall frequency analysis

MAUSAM ◽  
2022 ◽  
Vol 73 (1) ◽  
pp. 59-70
Author(s):  
N. VIVEKANANDAN
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Extreme Value ◽  
Qualitative Assessment ◽  
Likelihood Method ◽  
Extreme Value Analysis ◽  
Chi Square ◽  
Maximum Rainfall ◽  
Value Analysis ◽  
Family Of Distributions

Estimation of rainfall for a given return period is of utmost importance for planning and design of minor and major hydraulic structures. This can be achieved through Extreme Value Analysis (EVA) of rainfall by fitting Extreme Value family of Distributions (EVD) such as Generalized Extreme Value, Extreme Value Type-1, Extreme Value Type-2 and Generalized Pareto to the series of observed Annual 1-Day Maximum Rainfall (AMR) data. Based on the intended applications and the variate under consideration, Method of Moments (MoM), Maximum Likelihood Method (MLM) and L-Moments (LMO) are used for determination of parameters of probability distributions. The adequacy of fitting EVD to the AMR series was evaluated by quantitative assessment using Goodness-of-Fit (viz., Chi-square and Kolmogorov-Smirnov) and diagnostic test (viz., D-index) tests and qualitative assessment by the fitted curves of the estimated rainfall. The paper presents a study on intercomparison of EVD (using MoM, MLM and LMO) adopted in EVA of rainfall with illustrative example and the results obtained thereof. 

scholarly journals Assessing the Performance of Random Forests for Modeling Claim Severity in Collision Car Insurance

Risks ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 53
Author(s):  
Yves Staudt ◽  
Joël Wagner
Keyword(s):  
Random Forests ◽  
Goodness Of Fit ◽  
Generalized Additive Model ◽  
Mean Squared Error ◽  
Additive Model ◽  
Continuous Variables ◽  
Insurance Portfolio ◽  
Normal Transformation ◽  
Car Insurance ◽  
Log Normal

For calculating non-life insurance premiums, actuaries traditionally rely on separate severity and frequency models using covariates to explain the claims loss exposure. In this paper, we focus on the claim severity. First, we build two reference models, a generalized linear model and a generalized additive model, relying on a log-normal distribution of the severity and including the most significant factors. Thereby, we relate the continuous variables to the response in a nonlinear way. In the second step, we tune two random forest models, one for the claim severity and one for the log-transformed claim severity, where the latter requires a transformation of the predicted results. We compare the prediction performance of the different models using the relative error, the root mean squared error and the goodness-of-lift statistics in combination with goodness-of-fit statistics. In our application, we rely on a dataset of a Swiss collision insurance portfolio covering the loss exposure of the period from 2011 to 2015, and including observations from 81 309 settled claims with a total amount of CHF 184 mio. In the analysis, we use the data from 2011 to 2014 for training and from 2015 for testing. Our results indicate that the use of a log-normal transformation of the severity is not leading to performance gains with random forests. However, random forests with a log-normal transformation are the favorite choice for explaining right-skewed claims. Finally, when considering all indicators, we conclude that the generalized additive model has the best overall performance.

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

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.

scholarly journals 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)

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.

scholarly journals Frequency Analysis of Low Flows

1985 ◽  
Vol 16 (2) ◽  
pp. 105-128 ◽  
Author(s):  
G. V. Loganathan ◽  
C. Y. Kuo ◽  
T. C. McCormick
Keyword(s):  
Lower Bounds ◽  
Frequency Analysis ◽  
Probability Distributions ◽  
Flow Analysis ◽  
Extreme Value ◽  
Low Flow ◽  
Type Iii ◽  
Low Flows ◽  
Pearson Type

The transformations (i) SMEMAX (ii) Modified SMEMAX (iii) Power and Probability Distributions (iv) Weibull (α,β,γ) or Extreme value type III (v) Weibull (α,β,0) (vi) Log Pearson Type III (vii) Log Boughton are considered for the low flow analysis. Also, different parameter estimating procedures are considered. Both the Weibull and log Pearson can have positive lower bounds and thus their use in fitting low flow probabilities may not be physically justifiable. A new derivation generalizing the SMEMAX transformation is proposed. A new estimator for the log Boughton distribution is presented. It is found that the Boughton distribution with Cunnane's plotting position provides a good fit to low flows for Virginia streams.

scholarly journals Hujan rancangan berdasarkan analisis frekuensi regional dengan metode tl-moment

2017 ◽  
Vol 12 (1) ◽  
pp. 1-16
Author(s):  
Segel Ginting ◽  
William M Putuhena
Keyword(s):  
Frequency Analysis ◽  
Probability Distributions ◽  
Large Error ◽  
Extreme Value ◽  
Regional Frequency Analysis ◽  
Generalized Extreme Value ◽  
Generalized Pareto ◽  
Moment Ratio ◽  
Moments Method ◽  
Regional Frequency

The designstorm wereestimated by applying the regional frequency analysis provides benefits to a datasetwith limited amount of data has many advantages. Minimum data used in calculating the amount of design stromhas a very large error for higherreturn period. Therefore, the regional frequency analysis was used based on TL-moments method. There arethree types of probability distributions used in this study, namely the Generalized Extreme Value (GEV), Generalized Pareto (GPA) and the Generalized Logistic (GLO). Two of the three typesprobability distributions are the best choice by the TL-moment ratio diagrams which are Generalized Extreme Value, and Generalized Logistic. Ananother analysis wasconducted by the Z test and the Generalized Extreme Value (GEV) gives the best results. Therefore, the designs strom which was estimated based on the regional frequency analysis in Jakarta watersheds using the Generalized Extreme Value (GEV) has been determined.

scholarly journals Regional analysis of maximum rainfall using L-moment and LH-moment: A comparative case study for the northeast India

MAUSAM ◽  
2021 ◽  
Vol 68 (3) ◽  
pp. 451-462
Author(s):  
DHRUBA JYOTI BORA ◽  
MUNINDRA BORAH ◽  
ABHIJIT BHUYAN
Keyword(s):  
Frequency Analysis ◽  
Moment Method ◽  
Probability Distributions ◽  
Northeast India ◽  
Extreme Value ◽  
Generalized Extreme Value ◽  
Generalized Pareto ◽  
Rainfall Frequency ◽  
Best Fitting ◽  
Rainfall Frequency Analysis

Rainfall data of the northeast region of India has been considered for selecting best fit model for rainfall frequency analysis. The methods of L-moment has been employed for estimation of parameters five probability distributions, namely Generalized extreme value (GEV), Generalized Logistic(GLO), Pearson type 3 (PE3), 3 parameter Log normal (LN3) and Generalized Pareto (GPA) distributions. The methods of LH-moment of four orders (L1 L2, L3 & L4-moments) have also been used for estimating the parameters of three probability distributions namely Generalized extreme value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) distributions. PE3 distribution has been selected as the best fitting distribution using L-moment, GPA distribution using L1-moment and GLO distribution using L2, L3 & L4-moments. Relative root mean square error (RRMSE) and RBIAS are employed to compare between the results found from L-moment and LH-moment analysis. It is found that GPA distribution designated by L1-moment method is the most suitable and the best fitting distribution for rainfall frequency analysis of the northeast India. Also the L1-moment method is significantly more efficient than L-moment and other orders of LH-moment for rainfall frequency analysis of the northeast India.

scholarly journals Stochastic Generation of Low Stream Flow Data of Iokastis Stream, Kavala City, NE Greece

Proceedings ◽  
2018 ◽  
Vol 2 (11) ◽  
pp. 579
Author(s):  
Thomas Papalaskaris ◽  
Theologos Panagiotidis
Keyword(s):  
Stream Flow ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Specific Area ◽  
Low Flow ◽  
Urban Stream ◽  
Flow Data ◽  
Goodness Of Fit Tests ◽  
Chi Squared ◽  
Anderson Darling

Only a few scientific research studies, especially dealing with extremely low flow conditions, have been compiled so far, in Greece. The present study, aiming to contribute in this specific area of hydrologic investigation, generates synthetic low stream flow time series of an entire calendar year considering the stream flow data recorded during a center interval period of the year 2015. We examined the goodness of fit tests of eleven theoretical probability distributions to daily low stream flow data acquired at a certain location of the absolutely channelized urban stream which crosses the roads junction formed by Iokastis road an Chrisostomou Smirnis road, Agios Loukas residential area, Kavala city, NE Greece, using a 3-inches conventional portable Parshall flume and calculated the corresponding probability distributions parameters. The Kolmogorov-Smirnov, Anderson-Darling and Chi-Squared, GOF tests were employed to show how well the probability distributions fitted the recorded data and the results were demonstrated through interactive tables providing us the ability to effectively decide which model best fits the observed data. Finally, the observed against the calculated low flow data are plotted, compiling a log-log scale chart and calculate statistics featuring the comparison between the recorded and the forecasted low flow data.

Sign in / Sign up

Export Citation Format

Share Document