Goodness of fit tests for the skew-Laplace distribution

The skew-Laplace distribution is frequently used to fit the logarithm of particle sizes and it is also used in Economics, Engineering, Finance and Biology. We show the Anderson-Darling and Cramér-von Mises goodness of fit tests for this distribution

Power Comparison of Some Goodness-of-fit Tests

There are some existing commonly used goodness-of-fit tests, such as the Kolmogorov-Smirnov test, the Cramer-Von Mises test, and the Anderson-Darling test. In addition, a new goodness-of-fit test named G test was proposed by Chen and Ye (2009). The purpose of this thesis is to compare the performance of some goodness-of-fit tests by comparing their power. A goodness-of-fit test is usually used when judging whether or not the underlying population distribution differs from a specific distribution. This research focus on testing whether the underlying population distribution is an exponential distribution. To conduct statistical simulation, SAS/IML is used in this research. Some alternative distributions such as the triangle distribution, V-shaped triangle distribution are used. By applying Monte Carlo simulation, it can be concluded that the performance of the Kolmogorov-Smirnov test is better than the G test in many cases, while the G test performs well in some cases

Probability Distribution of Rainfall in Medan

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

Goodness of Fit Tests via Exponential Series Density Estimation

This paper explores the properties of a new nonparametric goodness of fit test, based on the likelihood ratio test of Portnoy (1988). It is applied via the consistent series density estimator of Crain (1974) and Barron and Sheu (1991). The asymptotic properties are established as trivial corollaries to the results of those papers as well as from similar results in Marsh (2000) and Claeskens and Hjort (2004). The paper focuses on the computational and numerical properties. Specifically it is found that the choice of approximating basis is not crucial and that the choice of model dimension, through consistent selection criteria, yields a feasible procedure. Extensive numerical experiments show that the usage of asymptotic critical values is feasible in moderate sample seizes. More importantly the new tests are shown to have significantly more power than established tests such as the Kolmogorov-Smirnov, Cramer-von Mises or Anderson-Darling. Indeed, for certain interesting alternatives the power of the proposed tests may be several times that of the established ones.

Testes de aderência aplicados à distribuição da profundidade de trinca em tubos do gerador de vapor de uma planta nuclear PWR

Steam generator tubes of nuclear power plants are periodically inspected as a risk and safety management strategy. The goal of this work was to verify the probability distribution model that better fits the crack depth, detected by the periodic inspection in steam generator tubes. For this, Kolmogorov-Smirnov and Anderson-Darling goodness-of-fit tests was applied to crack depth data, checking the normal, lognormal, Weibull, and exponential distribution models. The data sets obtained from inspections performed in two outages at one PWR nuclear power plant. The goodness-of-fit tests allowed to show that the crack depth data are better fitted to the Weibull distribution model.Tubos do gerador de vapor de plantas nucleares são inspecionados periodicamente como uma estratégia de gestão de risco e segurança. O objetivo deste trabalho foi verificar o modelo distribuição de probabilidade que melhor se ajusta à profundidade das trincas detectadas na inspeção periódica em tubos do gerador de vapor. Para tal, aplicaram-se ostestes de aderência de Kolmogorov-Smirnov e de Anderson-Darling aos dados da profundidade de trinca, verificando os modelos de distribuição normal, log-normal, de Weibull, e exponencial. Usaram-se os conjuntos de dados obtidos de inspeções realizadas em duas paradas de uma planta nuclear . Os testes de aderência permitiram mostrar que os dados da profundidade de trinca são melhor ajustados ao modelo de distribuição de Weibull

Using Statistics in Hydrology for Analyzing the outflow by Minitab ‎Program

الغرض من هذه الدراسة هو فحص استخدام الإحصاء في الهيدرولوجيا لتحليل تصريف التدفق الخارج في سد حديثة. تم استخدام إجمالي بيانات التدفق السنوي لمدة ثلاثين عامًا للفترة من 1991 إلى 2020. تم إنشاء معادلة رياضية لوظائف التوزيع الاحتمالي للبيانات. واستخدامت ثلاثة اختبارات هي Anderson-Darling و Ryan- Joiner) و Kolmogorov- Smirno) للتحقق من صحة البيانات، وقد تم إخضاع القيم المتوقعة لاختبار ملاءمة مثل kolmogorov-smirnov لتحديد التوزيع المناسب للبيانات. حسب اختبار K-s التوزيعات مناسبة للبيانات، لذا فإن جميع التوزيعات المجهزة كانت نموذجية للبيانات المستخدمة في هذه الدراسة بالاعتماد على اختبارK-SThe purpose of this study is to examine using statistics in hydrology for analyzing outflow discharge in Hadith Dam. Total annual outflow data of thirty years for period from 1991to 2020 were used. Mathematical equation for the probability distribution functions were established for the data. Three tests were used, namely (Anderson-Darling, Ryan- Joiner Similar to Shapiro-Wilk and Kolmogorov- Smirnov) to check the normality of the data; the predicted values were subjected to goodness of fit tests such as kolmogorov-smirnov to determine the distribution which is suitable for the data. Depending on the kolomogrov-smirnov (k-s) index, the distributions were suitable for the data, therefore, all the fitted distributions were typical for the data that were used in this paper depending on (k-s) index