Chi Square Goodness-of-Fit Test for the Poisson, Binomial and Negative Binomial Distributions

1979 ◽  
Vol 23 (3) ◽  
pp. 461-474 ◽  
Author(s):  
L. N. Bol’shev ◽  
M. Mirvaliev
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Binomial Distributions

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.

scholarly journals The analysis of FSH beta-subunit gene genotypes in East Anatolian Red, East Anatolian Red×Holstein, and Zavot bulls

2021 ◽  
Vol 2 (1) ◽  
pp. 91-97
Author(s):  
Sena Ardicli
Keyword(s):  
Population Genetics ◽  
Goodness Of Fit ◽  
Diversity Index ◽  
Fixation Index ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Genotypic Distribution ◽  
Test Population ◽  
Beta Subunit Gene ◽  
Index Level

Abstract This study aimed to investigate the genotypic distribution and population genetic parameters of the single nucleotide polymorphism (SNP) located on exon 3 at the FSHB gene in East Anatolian Red (EAR), East Anatolian Red×Holstein (EAR×H), and Zavot (Z) bulls. A total of 68 cattle including EAR (n=34), EAR×H (n=20), and Z (n=14) bulls were used. Genomic DNA was isolated from blood samples using the phenol/chloroform method. The genotyping of the SNP was carried out by the PCR-RFLP using the PstI restriction enzyme. Deviation from Hardy–Weinberg equilibrium (HWE) was calculated by using the chi-square goodness-of-fit test. Population genetics evaluation was performed for effective allele numbers, the polymorphism information content, theoretical heterozygosity, the fixation index, level of possible variability realization, and the Shannon-Weaver diversity index. In the present study, the AA and the AB genotypes were predominant in EAR and EAR×H bulls, respectively. Zavot breed was found to be monomorphic. There was a deviation from HWE, concerning the total cattle population. The population genetics evaluation showed that the marker was moderately informative for EAR and the crossbreeds, as well as the total population. Consequently, the polymorphism (rs207774587) within exon 3 of the bovine FSHB can be interpreted as a genetic marker with reliable variability for EAR and the crossbreeds, but not in Zavot cattle.

scholarly journals Modelling the number of olive groves in Spanish municipalities

2016 ◽  
Vol 14 (1) ◽  
pp. e0201
Author(s):  
Maria-Dolores Huete ◽  
Juan A. Marmolejo
Keyword(s):  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
External Factors ◽  
Discrete Distributions ◽  
Future Research ◽  
Total Output ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Total Variability ◽  
Olive Groves

<p>The univariate generalized Waring distribution (UGWD) is presented as a new model to describe the goodness of fit, applicable in the context of agriculture. In this paper, it was used to model the number of olive groves recorded in Spain in the 8,091 municipalities recorded in the 2009 Agricultural Census, according to which the production of oil olives accounted for 94% of total output, while that of table olives represented 6% (with an average of 44.84 and 4.06 holdings per Spanish municipality, respectively). UGWD is suitable for fitting this type of discrete data, with strong left-sided asymmetry. This novel use of UGWD can provide the foundation for future research in agriculture, with the advantage over other discrete distributions that enables the analyst to split the variance. After defining the distribution, we analysed various methods for fitting the parameters associated with it, namely estimation by maximum likelihood, estimation by the method of moments and a variant of the latter, estimation by the method of frequencies and moments. For oil olives, the chi-square goodness of fit test gives <em>p</em>-values of 0.9992, 0.9967 and 0.9977, respectively. However, a poor fit was obtained for the table olive distribution. Finally, the variance was split, following Irwin, into three components related to random factors, external factors and internal differences. For the distribution of the number of olive grove holdings, this splitting showed that random and external factors only account about 0.22% and 0.05%. Therefore, internal differences within municipalities play an important role in determining total variability.</p>

scholarly journals On the possibility of Benfordʼs Law application in accounting fraud detection

2020 ◽  
Vol 110 (166) ◽  
pp. 11-30
Author(s):  
Mateusz Baryła
Keyword(s):  
Research Method ◽  
Goodness Of Fit ◽  
Human Mind ◽  
Benford’S Law ◽  
Accounting Fraud ◽  
Process Data ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Polish Literature ◽  
Benford's Law

Purpose: The purpose of the article is to indicate that, theoretically and practically, Benford’s Law can be applied in order to detect accounting frauds. Methodology/approach: The paper provides an overview of current regulations and experts’ opinions published in the existing literature and internet sources. Moreover, data analysis was used as a research method. Findings: The results of assessing the conformity of the first two significant digits of distribution of foreign revenues from the sales of finished products to Benford’s Law (using the chi-square goodness of fit test) showed that in the case of a proper accounting process, one cannot reject the hypothesis that the data conform to Benford’s Law. On the other hand, the analysis of intentionally falsified foreign revenues led to the conclusion that in the case of an improper accounting process, data, in general, does not conform to Benford’s Law. Research limitations/implications: In the study, it was assumed that the human mind generates false val-ues of accounting entries, and the number of attempts to commit fraud was limited to 10. Originality/value: The article extends the existing knowledge of using Benfordʼs Law in detecting ac-counting fraud in the Polish literature.

scholarly journals PEMILIHAN DISTRIBUSI PROBABILITAS PADA ANALISA HUJAN DENGAN METODE GOODNESS OF FIT TEST

2016 ◽  
Vol 18 (2) ◽  
pp. 139-148
Author(s):  
Togani Cahyadi Upomo ◽  
Rini Kusumawardani
Keyword(s):  
Normal Distribution ◽  
Goodness Of Fit ◽  
Gumbel Distribution ◽  
Rainfall Event ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Pearson Iii Distribution

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.

The Application of the Chi-Square Test of Goodness-of-Fit to Mortality Data Graduated by Summation Formulae.

1971 ◽  
Vol 97 (2-3) ◽  
pp. 325-330 ◽  
Author(s):  
J. H. Pollard
Keyword(s):  
Degrees Of Freedom ◽  
Goodness Of Fit ◽  
Summation Formula ◽  
Mortality Data ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Summation Formulae ◽  
Chi Square Test

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.

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