Correction to: A generalized Anderson–Darling test for the goodness-of-fit evaluation of the fracture strain distribution of acrylic glass

Background: Suicide clusters at Cornell University and the Massachusetts Institute of Technology (MIT) prompted popular and expert speculation of suicide contagion. However, some clustering is to be expected in any random process. Aim: This work tested whether suicide clusters at these two universities differed significantly from those expected under a homogeneous Poisson process, in which suicides occur randomly and independently of one another. Method: Suicide dates were collected for MIT and Cornell for 1990–2012. The Anderson-Darling statistic was used to test the goodness-of-fit of the intervals between suicides to distribution expected under the Poisson process. Results: Suicides at MIT were consistent with the homogeneous Poisson process, while those at Cornell showed clustering inconsistent with such a process (p = .05). Conclusions: The Anderson-Darling test provides a statistically powerful means to identify suicide clustering in small samples. Practitioners can use this method to test for clustering in relevant communities. The difference in clustering behavior between the two institutions suggests that more institutions should be studied to determine the prevalence of suicide clustering in universities and its causes.

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Bootstrap Analysis

10.1093/oso/9780198505044.003.0004 ◽

2017 ◽

Author(s):

Russell Cheng

Keyword(s):

Goodness Of Fit ◽

Null Distribution ◽

Real Data ◽

Confidence Regions ◽

Confidence Bands ◽

Cumulative Distribution ◽

Attractive Alternative ◽

Bootstrap Analysis ◽

Parametric Bootstrapping ◽

Anderson Darling

Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit (GoF) tests, such as the Anderson-Darling A2 statistic whose null distribution is otherwise difficult to obtain, as it varies with different null hypotheses. A simple proof is given showing that the parametric BS is probabilistically exact for location-scale models. A formal regression lack-of-fit test employing parametric BS is given that can be used even when the regression data has no replications. Two real data examples are given.

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MENENTUKAN DISTRIBUSI REPRESENTATIF FREQUENSI CURAHAN HUJAN HARIAN MAKSIMUM DENGAN METODEHISTOGRAM DAN METODE PARAMETIK DI PROVINSI SUMATERA BARAT

Rang Teknik Journal ◽

10.31869/rtj.v1i1.608 ◽

2018 ◽

Vol 1 (1) ◽

Author(s):

Selpa Dewi

Keyword(s):

Goodness Of Fit ◽

Type Iii ◽

Pearson Type ◽

Chi Squared ◽

Anderson Darling

Penelitian ini bertujuan untuk menentukan distribusi yang representatif frequensi curahan hujan harian maksimum di Provinsi Sumatera Barat. Data yang digunakan untuk penelitian ini diambil dari data hujan maksimum harian selama 20 sampai 40 tahunan, dengan 24 stasiun penakar hujan untuk provinsi Sumatera Barat. Data masing-masing stasiun kemudian disusun dalam dua jenis deret data, yaitu deret data annual maxima dan deret data annual exceedances. Dari hasil uji deret data ini diharapkan mengikuti satu atau beberapa dari distribusi yang umum dipakai dalam hidrologi rekayasa, yaitu distribusi normal, normal-log, Gumbel, Gama-II, Gama-III dan distribusi Log-Pearson Type III (LP-III). Dengan mengunakan uji kecocokan (goodness of fit), uji parametrik, Chi-Squared test, Kolmogorov-Smirnovtest dan Anderson-Darling test ditambah dengan metode histrogram (visual).Kata kunci:Intensitas hujan distribusi representative annual maxima, annual exceendances, goodness of fitprovinsi Sumatera Barat.

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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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Statistical Analysis of In-Line Interaction of Closely Spaced Cylinder Arrays in Random Waves

Volume 2A: Structures, Safety, and Reliability ◽

10.1115/omae2020-18179 ◽

2020 ◽

Author(s):

Jiangnan Lu ◽

J. M. Niedzwecki

Keyword(s):

Goodness Of Fit ◽

Slenderness Ratio ◽

Steel Wire ◽

Relative Displacement ◽

Plastic Shell ◽

Random Waves ◽

Response Behavior ◽

Cylinder Arrays ◽

Waves And Currents ◽

Anderson Darling

Abstract Closely spaced cylinder arrays are widely used in offshore platform designs. When subject to random waves and currents, their interactive response behavior is very complicated and perhaps beyond the ability of direct analytical formulations to model their motions. In this study extremal statistics methods were utilized to analyze model basin data that investigated the response behavior of in-line paired and triple deep-water cylinder arrays. The cylinder models used in the model basin experiments were constructed with an ABS outer plastic shell that surrounded an inner steel wire core that could be pretensioned. The cylinder model diameter ratio of the outer shell to steel wire was 4.25 with a slenderness ratio of approximately 1300. The cylinder arrays were pretensioned on the top side and were tested varying pitch to diameter ratios of 3.0, 4.4, and 8.75. The random sea states were simulated using a JONSWAP spectrum. The response time series were investigated using generalized extreme value (GEV) distributions that were fitted to the block maxima that represented the maximum in-line relative displacement between two adjacent tendons. The most appropriate models were selected by comparing their goodness of fit via the Anderson-Darling (AD) test criterion with special attentions paid to their performance in fitting the upper tail of the distribution. The selected models were then used to predict threshold-crossing probabilities of the cylinder array relative response behavior. Both tabular and graphical interpretations of the findings are presented and discussed.

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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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Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data

Astin Bulletin ◽

10.1017/s0515036100013519 ◽

2003 ◽

Vol 33 (2) ◽

pp. 365-381 ◽

Cited By ~ 19

Author(s):

Vytaras Brazauskas ◽

Robert Serfling

Keyword(s):

Goodness Of Fit ◽

Real Data ◽

Efficient Estimation ◽

Small Samples ◽

Robust Estimators ◽

Trade Offs ◽

Pareto Model ◽

Kolmogorov Smirnov ◽

Anderson Darling ◽

Von Mises

Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.

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Goodness of Fit Tests for Marshal-Olkin Extended Rayleigh Distribution

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v16i3.2624 ◽

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.

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

Proceedings ◽

10.3390/proceedings2110579 ◽

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.

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