scholarly journals A generalized Anderson–Darling test for the goodness-of-fit evaluation of the fracture strain distribution of acrylic glass

2021 ◽  
Author(s):  
Marcel Berlinger ◽  
Stefan Kolling ◽  
Jens Schneider
Keyword(s):  
Goodness Of Fit ◽  
Tensile Tests ◽  
Distribution Functions ◽  
Image Correlation ◽  
Strain Behavior ◽  
Probability Estimator ◽  
Goodness Of Fit Tests ◽  
Static Tensile ◽  
Structural Parts ◽  
Anderson Darling

AbstractAcrylic glasses, as well as mineral glasses, exhibit a high variability in tensile strength. To cope with this uncertainty factor for the dimensioning of structural parts, modeling of the stress-strain behavior and a proper characterization of the varying fracture stress or strain are required. For the latter, this work presents an experimental and mathematical methodology. Fracture strains from 50 quasi-static tensile tests, locally analyzed using digital image correlation, form the sample. For the assignment of an occurrence probability to each experiment, an evaluation of existing probability estimators is conducted, concerning their ability to fit selected probability distribution functions. Important goodness-of-fit tests are introduced and assessed critically. Based on the popular Anderson-Darling test, a generalized form is proposed that allows a free, hitherto not possible, choice of the probability estimator. To approach the fracture strains population, the combination of probability estimator and distribution function that best reproduces the experimental data is determined, and its characteristic progression is discussed with the aid of fractographic analyses.

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

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.

Temporal and spatial variations in annual rainfall distribution in Erbil province

2018 ◽  
Vol 47 (1) ◽  
pp. 59-67
Author(s):  
Tariq H Karim ◽  
Dawod R Keya ◽  
Zahir A Amin
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Kendall Test ◽  
Distribution Functions ◽  
Annual Rainfall ◽  
Maximum Rainfall ◽  
Probability Distribution Functions ◽  
Goodness Of Fit Tests ◽  
Annual Maximum Rainfall ◽  
Best Fit

This study aimed to determine the best fit probability distribution of annual maximum rainfall using data from nine stations within Erbil province using different statistical analyses. Nine commonly used probability distribution functions, namely Normal, Lognormal (LN), one-parameter gamma (1P-G), 2P-G, 3P-G, Log Pearson, Weibull, Pareto, and Beta, were assessed. On the basis of maximum overall score, obtained by adding individual point scores from three selected goodness-of-fit tests, the best fit probability distribution was identified. Results showed that the 2P-G distribution and LN distribution were the best fit probability distribution functions for annual rainfall for the region. The analysis of annual rainfall records in Erbil city spanning from 1964 to 2013, covering three periods, also revealed significant temporal changes in the shape and scale parameter patterns of the fitted gamma distribution. Based on the reliable annual rainfall data in the region, the shape and scale parameters were then regionalized, hence it is possible to find the parameter values for any desired location within the study area. The Mann–Kendall test results indicated that there was a decreasing trend in rainfall over most of the study area in recent decades.

scholarly journals Goodness of Fit Tests for Marshal-Olkin Extended Rayleigh Distribution

2019 ◽  
pp. 587-598
Author(s):  
Naz Saud ◽  
Sohail Chand
Keyword(s):  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Rayleigh Distribution ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Estimated Parameters ◽  
Percentage Points ◽  
Anderson Darling ◽  
Von Mises

A class of goodness of fit tests for Marshal-Olkin Extended Rayleigh distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. For determination of asymptotic percentage points, Kolomogorov-Sminrov, Cramer-von-Mises, Anderson-Darling,Watson, and Liao-Shimokawa test statistic are used. This article uses Monte Carlo simulations to obtain asymptotic percentage points for Marshal-Olkin extended Rayleigh distribution. Moreover, power of the goodness of fit test statistics is investigated for this lifetime model against several alternatives.

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.

Robust bi-level risk-based optimal scheduling of microgrid operation against uncertainty

2020 ◽  
Vol 54 (4) ◽  
pp. 993-1012 ◽  
Author(s):  
Hêriș Golpîra ◽  
Salah Bahramara ◽  
Syed Abdul Rehman Khan ◽  
Yu Zhang
Keyword(s):  
Risk Aversion ◽  
Value At Risk ◽  
Goodness Of Fit ◽  
Distribution Functions ◽  
Optimal Scheduling ◽  
Conditional Value At Risk ◽  
Optimization Approach ◽  
Goodness Of Fit Tests ◽  
The Cost ◽  
Initial Objective

The model introduced in this paper is the first to propose a decentralized robust optimal scheduling of MG operation under uncertainty and risk. The power trading of the MG with the main grid is the first stage variable and power generation of DGs and power charging/discharging of the battery are the second stage variables. The uncertain term of the initial objective function is transformed into a constraint using robust optimization approach. Addressing the Decision Maker’s (DMs) risk aversion level through Conditional Value at Risk (CVaR) leads to a bi-level programming problem using a data-driven approach. The model is then transformed into a robust single-level using Karush–Kahn–Tucker (KKT) conditions. To investigate the effectiveness of the model and its solution methodology, it is applied on a MG. The results clearly demonstrate the robustness of the model and indicate a strong almost linear relationship between cost and the DMs various levels of risk aversion. The analysis also outlines original characterization of the cost and the MGs behavior using three well-known goodness-of-fit tests on various Probability Distribution Functions (PDFs), Beta, Gumbel Max, Normal, Weibull, and Cauchy. The Gumbel Max and Normal PDFs, respectively, exhibit the most promising goodness-of-fit for the cost, while the power purchased from the grid are well fitted by Weibull, Beta, and Normal PDFs, respectively. At the same time, the power sold to the grid is well fitted by the Cauchy PDF.

scholarly journals A Probabilistic Approach to the Simulation of Non-Linear Stress-Strain Relationships for Oriented Strandboard Subject to In-Plane Tension

2011 ◽  
Vol 478 ◽  
pp. 54-63 ◽  
Author(s):  
Antony T. McTigue ◽  
Annette M. Harte
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Regression Equations ◽  
Goodness Of Fit Tests ◽  
Oriented Strandboard ◽  
Anderson Darling ◽  
Standardised Testing ◽  
Tension Loading ◽  
Tension Strength

This paper presents the results from an experimental test program conducted on commercially available oriented strandboard (OSB) panels and statistical analyses of the results. Standardised testing was used to determine the short-term behaviour of OSB/3 panels subjected to tension loading. A variety of thicknesses sourced from three different producers were used. Analysis of the results indicate that a quadratic expression in the form of  = a2 + b provides the best description of the relationship between stress (and strain ( up to the point of failure. It has also been shown that the coefficients a and b of the quadratic regression equations are negatively correlated to each other. Anderson-Darling goodness-of-fit tests were conducted on the results for tension strength and modulus of elasticity (MOE). The results indicate that the tension strength and MOE come from populations that follow either normal or lognormal probability distributions.

scholarly journals Goodness-of-fit tests for the beta Gompertz distribution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 69-81
Author(s):  
Hanaa Abu-Zinadah ◽  
Asmaa Binkhamis
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Gompertz Distribution ◽  
Goodness Of Fit Tests ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

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