scholarly journals Evaluating Rank Histograms Using Decompositions of the Chi-Square Test Statistic

2008 ◽  
Vol 136 (6) ◽  
pp. 2133-2139 ◽  
Author(s):  
Ian T. Jolliffe ◽  
Cristina Primo

Abstract Rank histograms are often plotted to evaluate the forecasts produced by an ensemble forecasting system—an ideal rank histogram is “flat” or uniform. It has been noted previously that the obvious test of “flatness,” the well-known χ2 goodness-of-fit test, spreads its power thinly and hence is not good at detecting specific alternatives to flatness, such as bias or over- or underdispersion. Members of the Cramér–von Mises family of tests do much better in this respect. An alternative to using the Cramér–von Mises family is to decompose the χ2 test statistic into components that correspond to specific alternatives. This approach is described in the present paper. It is arguably easier to use and more flexible than the Cramér–von Mises family of tests, and does at least as well as it in detecting alternatives corresponding to bias and over- or underdispersion.

2016 ◽  
Vol 18 (2) ◽  
pp. 139-148
Author(s):  
Togani Cahyadi Upomo ◽  
Rini Kusumawardani

Rainfall event is a stochastic process, so to explain and analyze this processes the probability theory and frequency analysisare used. There are four types of probability distributions.They are normal, log normal, log Pearson III and Gumbel. To find the best probabilities distribution, it will used goodness of fit test. The tests consist of chi-square and smirnov-kolmogorov. Results of the chi-square test for normal distribution, log normal and log Pearson III was 0.200, while for the Gumbel distribution was 2.333. Results of Smirnov Kolmogorov test for normal distribution D = 0.1554, log-normal distribution D = 0.1103, log Pearson III distribution D = 0.1177 and Gumbel distribution D = 0.095. All of the distribution can be accepted with a confidence level of 95%, but the best distribution is log normal distribution.Kejadian hujan merupakan proses stokastik, sehingga untuk keperluan analisa dan menjelaskan proses stokastik tersebut digunakan teori probabilitas dan analisa frekuensi. Terdapat empat jenis distribusi probabilitas yaitu distribusi normal, log normal, log pearson III dan gumbel. Untuk mencari distribusi probabilitas terbaik maka akan digunakan pengujian metode goodness of fit test. Pengujian tersebut meliputi uji chi-kuadrat dan uji smirnov kolmogorov. Hasil pengujian chi kuadrat untuk distribusi normal, log normal dan log pearson III adalah 0.200, sedangkan untuk distribusi gumbel 2.333. Hasil pengujian smirnov kolmogorov untuk distribusi normal dengan nilai D = 0.1554, distribusi log normal dengan nilai D = 0.1103, distribusi log pearson III dengan nilai D = 0.1177 dan distribusi gumbel dengan nilai D = 0.095. Seluruh distribusi dapat diterima dengan tingkat kepercayaan 95%, tetapi distribusi terbaik adalah distribusi log normal.


1971 ◽  
Vol 97 (2-3) ◽  
pp. 325-330 ◽  
Author(s):  
J. H. Pollard

In his paper of 1941, Seal included details of some experiments he performed in an attempt to estimate the appropriate number of degrees of freedom for the chi-square goodness-of-fit test of a summation formula graduation. These results are referred to by Tetley and by Benjamin and Haycocks in their textbooks when they mention the difficulty of determining the number of degrees of freedom or mean chi-square value.


Author(s):  
Naz Saud ◽  
Sohail Chand

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.


Author(s):  
Khaoula Aidi ◽  
Nadeem Shafique Butt ◽  
Mir Masoom Ali ◽  
Mohamed Ibrahim ◽  
Haitham M. Yousof ◽  
...  

A new modified version of the Bagdonavičius-Nikulin goodness-of-fit test statistic is presented for validity for the right censor case under the double Burr type X distribution. The maximum likelihood estimation method in censored data case is used and applied. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right censored estimation method. Another simulation study is presented for testing the null hypothesis under the modified version of the Bagdonavičius and Nikulin goodness-of-fit statistical test. Four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation.


Blood ◽  
2005 ◽  
Vol 106 (11) ◽  
pp. 2647-2647
Author(s):  
Yu-Min Shen ◽  
Anna Dyszkiewicz-Korpanty ◽  
Ray Lee ◽  
Jyoti Balani ◽  
Eugene Frenkel ◽  
...  

Abstract AIMS: We investigated the prevalence and clinical relevance and significance of the various immunoglobulin (Ig) isotypes of the different aPLs and lupus anticoagulant (LAC). METHOD: Our study registry for the year 2003 included 472 patients who had a complete antiphospholipid antibody laboratory work up and clinical evaluation. 137 had the presence of LAC, detected by the dilute Russell’s viper venom time (Dade Behring, Marburg, Germany), PTT-LA (Diagnostica Stago, Asnieres, France), or hexagonal phospholipid neutralization test (Diagnostica Stago, Asnieres, France); 211 had elevated titers of antibodies of IgG, IgM or IgA isotypes against cardiolipin (aCL), phosphatidylserine (aPS), or β2-glycoprotein-I (aβ2GPI), detected by ELISA (Corgenix, Inc, Westminister, CO, USA). 204 had no evidence of either LAC or aPL. RESULTS: Of the patients with aPL, 67 (32%) had elevated titers of IgG, 126 (60%) had IgM, and 118 (56%) had IgA. Thrombotic events occurred in 61% (41 of 67), 52% (65 of 126), and 61% (72 of 118) of the patients with IgG, IgM, and IgA respectively. Patients with IgG and IgA isotypes of aCL, aPS and aβ2GPI had higher rates (58–67%) of thrombotic events (see table 1) than patients with IgM isotypes (46–50%). Stepwise logistic regression analysis identified elevated titer of IgA of any aPL as an independent risk factor for thrombosis (see table 2), even in the absence of LAC. Thrombotic events observed include deep venous thrombosis (25%), pulmonary embolism (12%), cerebrovascular accident (50%), myocardial infarction (8%), and peripheral arterial occlusion (3%); pregnancy complication, retinal vascular thrombosis, and dialysis access thrombosis were also seen. CONCLUSION: Our study demonstrates that aPL of IgA isotype is prevalent and significantly associated with thrombotic events. Proportions of Patients with Thrombosis amongst various aPLs and Ig Isotypes aCL aPS aβ2GPI Total * Two-sided P < 0.05 by McNemar’s test for equality of two dependent proportions IgG 28/43 (65%) 23/36 (64%) 13/21 (62%)* 41/67 (61%) IgM 17/37 (46%)* 28/58 (48%) 45/90 (50%)* 65/126 (52%) IgG 15/26 (58%)* 22/33 (67%) 54/91 (59%)* 72/118 (61%) Total 44/79 (56%) 58/105 (55%) 85/159 (53%) 118/211 (56%) Risk Factors for Thrombosis Antibody Odds Ratio 95% Wald Confidence Limit * p < 0.05 by the Wald chi-square test. Hosmer and Lemeshow goodness-of-fit test was used to assess the model fit. N=472 for the 1st four analyses, N=335 for the last three analyses. LAC 1.627 1.073–2.466* IgG regardless of LAC 1.364 0.781–2.384 IgM regardless of LAC 0.874 0.569–1.344 IgA regardless of LAC 1.587 1.012–2.490* IgG LAC negative 1.790 0.863–3.714 IgM LAC negative 0.878 0.515–1.499 IgA LAC negative 1.812 1.035–3.172*


2016 ◽  
Vol 6 (2) ◽  
pp. 1-20 ◽  
Author(s):  
Parviz Kafchehi ◽  
Kaveh Hasani ◽  
Arman Gholami

The aim of this study is to investigate the relationship between innovation orientation and strategic typology in firms such a way that a classification on the organization's orientation toward innovation and strategy could be obtained. The statistical population includes high executive managers of firms who have been acting in 4 industries of banking (B), food (F), insurance (I), and pharmacy (P), and have been the five pioneering firms in these industries. To test the hypothesis, the mean test analysis, the Goodness- of- Fit- Test, Chi- square test, and cross- tables were used and tested by SPSS18 software. The results show that there is a significant relationship between the firm's orientation toward innovation and competitive strategy; the more firm's orientation toward innovation, the firms uses more Prospector strategy, and their strategies have a more aggressive state. This paper provides a richer understanding of innovation orientation and strategic typology formation for similar firms.


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