A New Goodness-of-Fit Test for Grouped Data

2012 ◽  
Vol 569 ◽  
pp. 455-460
Author(s):  
Jin Qin ◽  
Jun Yang
Keyword(s):  
Goodness Of Fit ◽  
Test Method ◽  
Ratio Method ◽  
Grouped Data ◽  
Survival Ratio ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Distribution Type ◽  
Smirnov Test

In data analysis of reliability, the traditional goodness-of-fit test is not applicable for grouped data under some circumstances. In this paper, a Kolmogorov-Smirnov test based on survival ratio method is proposed to determine the distribution type of grouped data. The power of the proposed test and other well-known goodness-of-fit tests are compared by Monte Carlo simulation, and the results show that the proposed test method is more powerful.

AN ALTERNATIVE TEST FOR UNIFORMITY

2009 ◽  
Vol 16 (04) ◽  
pp. 343-356 ◽  
Author(s):  
ZHENMIN CHEN ◽  
CHUNMIAO YE
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Integral Transformation ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Underlying Distribution ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Alternative Test ◽  
Smirnov Test

Improving power of goodness-of-fit tests is an important research topic in statistics. The goal of the goodness-of-fit test is to check whether the underlying probability distribution, from which a sample is drawn, differs from a hypothesized distribution. Numerous research papers have been published in this area. It has been shown that the power of the existing goodness-of-fit tests in the literature is unsatisfactory when the alternative distributions are of V-shape or when the sample sizes are small. This motivates the development of more powerful test statistics. In this research, a new test statistic is proposed. The result can be used to test whether the underlying probability distribution differs from a uniform distribution. By applying the probability integral transformation, the proposed test statistic can be used to check whether the underlying distribution differs from any hypothesized distribution. The performance of the method proposed in this research is compared with the Kolmogorov–Smirnov test, which is a widely adopted statistical test in the literature. It has been shown that the test proposed in this proposal is more powerful than the Kolmogorov–Smirnov test in some cases.

scholarly journals A Cautionary Note on the Use of the Kolmogorov–Smirnov Test for Normality

2007 ◽  
Vol 135 (3) ◽  
pp. 1151-1157 ◽  
Author(s):  
Dag J. Steinskog ◽  
Dag B. Tjøstheim ◽  
Nils G. Kvamstø
Keyword(s):  
Goodness Of Fit ◽  
Small Sample ◽  
Power Comparison ◽  
Goodness Of Fit Test ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Small Sample Problem ◽  
Tests For Normality ◽  
Test For Normality ◽  
Smirnov Test

Abstract The Kolmogorov–Smirnov goodness-of-fit test is used in many applications for testing normality in climate research. This note shows that the test usually leads to systematic and drastic errors. When the mean and the standard deviation are estimated, it is much too conservative in the sense that its p values are strongly biased upward. One may think that this is a small sample problem, but it is not. There is a correction of the Kolmogorov–Smirnov test by Lilliefors, which is in fact sometimes confused with the original Kolmogorov–Smirnov test. Both the Jarque–Bera and the Shapiro–Wilk tests for normality are good alternatives to the Kolmogorov–Smirnov test. A power comparison of eight different tests has been undertaken, favoring the Jarque–Bera and the Shapiro–Wilk tests. The Jarque–Bera and the Kolmogorov–Smirnov tests are also applied to a monthly mean dataset of geopotential height at 500 hPa. The two tests give very different results and illustrate the danger of using the Kolmogorov–Smirnov test.

A new method for process control based on goodness of fit tests

2015 ◽  
Vol 32 (2) ◽  
pp. 132-143
Author(s):  
Mohammad Saleh Owlia ◽  
Mohammad Saber Fallah Nezhad ◽  
Mohesn Sheikh Sajadieh
Keyword(s):  
Process Control ◽  
Design Methodology ◽  
Goodness Of Fit ◽  
New Method ◽  
Content Type ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Shift Detection ◽  
The Subject ◽  
Smirnov Test

Purpose – The purpose of this paper is to propose a new method based on goodness of fit tests for shift detection problems. Design/methodology/approach – In this method, although the distribution of gathered data from the process is the subject of control, but any out-of-control signal could also be generalized to the overall state of the process including the parameters of the distribution. Findings – Results of simulation study denote that among goodness of fit tests, the χ2 test has a better performance than the Kolmogorov-Smirnov test in detecting shifts of process. Also comparison of proposed method with traditional methods denotes that, proposed method generally has smaller probabilities of first and second type errors. Originality/value – To the best of author’s knowledge, no attention has previously been paid to application of goodness of fit tests in process control.

scholarly journals El entrenamiento de la resistencia y sus efectos en la competición en la altura en el fútbol ecuatoriano (Endurance training and its effects in competition at altitude in the Ecuadorian soccer)

Retos ◽  
2017 ◽  
pp. 221-227
Author(s):  
Manuel Gutierrez Cruz ◽  
Lisbet Guillen Pereira ◽  
Flavio Antonio Perlaza ◽  
José Ramón Guerra Santiesteban ◽  
Giovanny Capote Lavandero ◽  
...  
Keyword(s):  
Endurance Training ◽  
Goodness Of Fit ◽  
Technical Skills ◽  
Three Dimensions ◽  
Maximum Volume ◽  
Goodness Of Fit Test ◽  
Four Dimensions ◽  
Kolmogorov Smirnov ◽  
Student’S T ◽  
Smirnov Test

La investigación se realizó en el equipo de la reserva del Barcelona Sporting Club del fútbol ecuatoriano de primera división, cuyo objetivo se enfocó en validar una alternativa metodológica para el entrenamiento de la resistencia con vista a la competición en la altura, para ello se asumió un pre-experimento el cual permitió evaluar cuatro dimensiones, la primera relacionada con el conocimiento sobre el entrenamiento de resistencia para la competición en la altura; en este aspecto se trabajó con el cuerpo técnico del equipo. De igual forma intervino una muestra de 12 futbolistas seleccionados mediante un muestreo intencional, en esta se evaluaron tres dimensiones: la efectividad de las acciones ofensivas y defensivas, la segunda  analiza la cantidad de metros recorridos (Test de Cooper) y la tercera el VO2. Para el análisis estadístico de los datos se utilizó un test de bondad de ajustes (test de Kolmogorov-Smirnov: KS), los resultados permitieron aplicar un test paramétrico (T de Student). En cada una de las dimensiones analizadas los resultados arrojados fueron significativos siendo p=.000. Para el análisis estadístico se empleó el paquete SPSS 23.0. Los resultados del estudio demostraron como resultado de la aplicación de la propuesta un incremento en la efectividad en la utilización de la técnica para  crear y solucionar situaciones en los últimos 15 minutos de juego, en concordancia se observó  un mejor estado de las manifestaciones externas de la carga física y la capacidad de resistencia aerobia a partir del incremento del VO2.Summary: The research was carried out with the reserve team of Barcelona Sporting Club from the Ecuadorian soccer first division. The objective was to validate a methodological alternative for endurance training focused on competitions at altitude. The pre-experimental design of the study was directed to evaluating four dimensions. The first one concerned developing knowledge about endurance training for competitions at altitude; in this aspect, we worked with the technical staff of the team. In the same way, a sample of 12 players was selected using intentional sampling, three dimensions being evaluated: effectiveness of offensive and defensive actions; meters covered (Cooper test); and maximum volume of oxygen (VO2). Data analysis was based on goodness of fit test (Kolmogorov-Smirnov test [KS]). Data normality allowed to apply parametric tests (Student's T). Results were significant in each of the analyzed dimensions, being p = .000. SPSS 23.0 package was used for statistical analysis. Results of the implementation of the method demonstrated an increased effectiveness in using technical skills to create and solve situations in the last 15 minutes of the matches, at the same time as we could observe a better state of the external manifestations of physical load as well as improved capacity of aerobic endurance derived from the increase in VO2.

scholarly journals Performances of Shannon’s Entropy Statistic in Assessment of Distribution of Data

2017 ◽  
Vol 28 (2) ◽  
pp. 30-42 ◽  
Author(s):  
Lorentz Jäntschi ◽  
Sorana D. Bolboacă
Keyword(s):  
Experimental Data ◽  
Goodness Of Fit ◽  
Error Function ◽  
Shannon’S Entropy ◽  
Goodness Of Fit Test ◽  
Shannon's Entropy ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

AbstractStatistical analysis starts with the assessment of the distribution of experimental data. Different statistics are used to test the null hypothesis (H0) stated as Data follow a certain/specified distribution. In this paper, a new test based on Shannon’s entropy (called Shannon’s entropy statistic, H1) is introduced as goodness-of-fit test. The performance of the Shannon’s entropy statistic was tested on simulated and/or experimental data with uniform and respectively four continuous distributions (as error function, generalized extreme value, lognormal, and normal). The experimental data used in the assessment were properties or activities of active chemical compounds. Five known goodness-of-fit tests namely Anderson-Darling, Kolmogorov-Smirnov, Cramér-von Mises, Kuiper V, and Watson U2 were used to accompany and assess the performances of H1.

scholarly journals PEMODELAN DISTRIBUSI FREKWENSI TIME HEADWAY LALU LINTAS DI WILAYAH JALAN BERBUKIT

2016 ◽  
Vol 12 (2) ◽  
pp. 71
Author(s):  
Rizky Indra Utama ◽  
Purnawan Purnawan ◽  
Hendra Gunawan
Keyword(s):  
Goodness Of Fit ◽  
Traffic Simulation ◽  
Test Model ◽  
Goodness Of Fit Test ◽  
Microscopic Traffic Simulation ◽  
Time Headway ◽  
Kolmogorov Smirnov ◽  
Data Program ◽  
Smirnov Test

Time headway merupakan besaran mikroskopik arus lalu lintas yang sangat penting kegunaannya dalam analisis dan perencanaan suatu sistem transportasi. Pentingnya time headway, khususnya dalam microscopic traffic simulation, mendorong perlunya penentuan standar nilai yang dapat digunakan untuk keperluan praktis. Penelitian ini bertujuan untuk mengetahui model distribusi time headway yang sesuai untuk data hasil penelitian di wilayah jalan berbukit. Penelitian mengambil data arus lalu lintas pada ruas jalan Padang Panjang– Bukittinggi Km. 5. Pengumpulan data primer dilakukan dengan menggunakan handycam. Pengolahan data pengamatan menggunakan Software Stop Data Program. Untuk mendapatkan goodness of fit dari model distribusi data pengamatan yang cocok dengan distribusi teoritis, maka dilakukan Kolmogorov Smirnov Test (K-S Test) dengan menggunakan Software EasyFit, sehingga dihasilkan model yang cocok dengan kondisi wilayah jalan berbukit. Dari analisis didapatkan hasil sebagai berikut: model distribusi terbaik hasil uji time headway individual Hari Sabtu pada jalur tanjakan didapatkan model hasil uji yang terbaik adalah model Beta dengan nilai α1=2,290 ,α2=7,668 , 􀜽 =4,615 􀵈10􀬿􀬵􀬻, 􀜾 =16,809, pada jalur turunan didapatkan model hasil uji yang terbaik adalah model Weibull dengan nilai α= 1,546 ,β=3,551 ,γ = 0. Model distribusi terbaik hasil uji time headway individual Hari Minggu pada jalur tanjakan didapatkan model hasil uji yang terbaik adalah model Beta dengan nilai α1=2,217 ,α2=6,626 ,􀜽=2,895􀵈10􀬿􀬵􀬺 ,􀜾 =15,046, untuk jalur turunan didapatkan model hasil uji yang terbaik adalah model Cauchy dengan nilai σ=0,703 dan μ=2,937.Time headway rata-rata Hari Sabtu pada jalur tanjakan diperoleh 3,86 detik, pada jalur turunan didapatkan 3,17 detik. Selanjutnya time headway rata-rata Hari Minggu pada jalur tanjakan didapatkan 3,77 detik, pada jalur turunan diperoleh 3,21 detik.Kata kunci : Time Headway, Goodness Of Fit Test, Model Distribusi

scholarly journals Comparison of Goodness of Fit Tests for Normal Distribution

2018 ◽  
pp. 1-32
Author(s):  
I. Agu, Friday ◽  
E. Francis, Runyi
Keyword(s):  
Normal Distribution ◽  
Goodness Of Fit ◽  
P Value ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov

Goodness of fit test is a test that has attracted researchers’ interest over the decades. This study is on goodness of fit test for normal distribution only. The Kolmogorov-Smirnov (K-St) and Pearson’s Chi-square (χ² test) goodness of fit test were used to determine the normality of a given data.  The result revealed that the data is normal under the two tests and that the Kolmogorov-Smirnov (K-S test) were preferred to Pearson’s Chi-square (χ² test). The Kolmogorov-Smirnov (K-S) test of goodness of fit is the most suitable in terms of the p-value.  

scholarly journals Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Masoumeh Akbari
Keyword(s):  
Order Statistics ◽  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Probability Function ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Definition Of ◽  
Von Mises ◽  
First Moment

In this paper, a new definition of the number of observations near the kth order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions xn,0<x<1,n≥1. Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations.

scholarly journals Raking-ratio empirical process with auxiliary information learning

2020 ◽  
Vol 24 ◽  
pp. 435-453
Author(s):  
Mickael Albertus
Keyword(s):  
Asymptotic Behavior ◽  
Goodness Of Fit ◽  
Empirical Process ◽  
Information Source ◽  
Auxiliary Information ◽  
Computational Method ◽  
Empirical Measure ◽  
Ratio Method ◽  
Goodness Of Fit Test ◽  
Chi Square

The raking-ratio method is a statistical and computational method which adjusts the empirical measure to match the true probability of sets of a finite partition. The asymptotic behavior of the raking-ratio empirical process indexed by a class of functions is studied when the auxiliary information is given by estimates. These estimates are supposed to result from the learning of the probability of sets of partitions from another sample larger than the sample of the statistician, as in the case of two-stage sampling surveys. Under some metric entropy hypothesis and conditions on the size of the information source sample, the strong approximation of this process and in particular the weak convergence are established. Under these conditions, the asymptotic behavior of the new process is the same as the classical raking-ratio empirical process. Some possible statistical applications of these results are also given, like the strengthening of the Z-test and the chi-square goodness of fit test.

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