scholarly journals A Least Squares Estimation Method for the Linear Learning Model

1978 ◽  
Vol 15 (1) ◽  
pp. 145-153
Author(s):  
Berend Wierenga
Keyword(s):  
Least Squares ◽  
Simulation Study ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Estimation Method ◽  
Learning Model ◽  
New Method ◽  
Data Sets ◽  
Goodness Of Fit Test ◽  
Chi Square

The author presents a new method for estimating the parameters of the linear learning model. The procedure, essentially a least squares method, is easy to carry out and avoids certain difficulties of earlier estimation procedures. Applications to three different data sets are reported, as well as results from a goodness-of-fit test. A simulation study was carried out to validate the method. The outcomes are compared with those obtained from the minimum chi square estimation method. The results of the new method appear to be satisfactory.

scholarly journals A Modified Chi-square Type Test Statistic for the Double Burr X Model with Applications to Right Censored Medical and Reliability Data

2021 ◽  
pp. 615-623
Author(s):  
Khaoula Aidi ◽  
Nadeem Shafique Butt ◽  
Mir Masoom Ali ◽  
Mohamed Ibrahim ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Right Censored Data ◽  
The Right

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.

scholarly journals Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1949
Author(s):  
Mukhtar M. Salah ◽  
M. El-Morshedy ◽  
M. S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Least Square Estimation ◽  
Chi Square ◽  
Anderson Darling ◽  
The Right

The extreme value theory is expanded by proposing and studying a new version of the Fréchet model. Some new bivariate type extensions using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula, and Renyi’s entropy copula are derived. After a quick study for its properties, different non-Bayesian estimation methods under uncensored schemes are considered, such as the maximum likelihood estimation method, Anderson–Darling estimation method, ordinary least square estimation method, Cramér–von-Mises estimation method, weighted least square estimation method, left-tail Anderson–Darling estimation method, and right-tail Anderson–Darling estimation method. Numerical simulations were performed for comparing the estimation methods using different sample sizes for three different combinations of parameters. The Barzilai–Borwein algorithm was employed via a simulation study. Three applications were presented for measuring the flexibility and the importance of the new model for comparing the competitive distributions under the uncensored scheme. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. The modified goodness-of-fit statistic test was applied for the right censored real data set, called leukemia free-survival times for autologous transplants. Based on the maximum likelihood estimators on initial data, the modified goodness-of-fit test recovered the loss in information while the grouping data and followed chi-square distributions. All elements of the modified goodness-of-fit criteria tests are explicitly derived and given.

scholarly journals A Modified Chi-square Type Test for Distributional Validity with Applications to Right Censored Reliability and Medical Data

2021 ◽  
pp. 1113-1121 ◽  
Author(s):  
Haitham M. Yousof ◽  
Abdullah H. Al-nefaie ◽  
Khaoula Aidi ◽  
M. Masoom Ali ◽  
Mohamed ibrahim Mohamed
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Data Sets ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Right Censored Data ◽  
Type Test ◽  
The Right ◽  
New Distribution

In this paper, a modified Chi-square goodness-of-fit test called the modified Bagdonavičius-Nikulin goodness-of-fit test statistic is investigated and the applied for distributional validation under the right censored case. The new modified goodness-of-fit test is presented and applied for the right censored data sets. The algorithm of the censored Barzilai-Borwein is employed via a comprehensive simulation study for assessing validity of the new test. The modified Bagdonavičius-Nikulin test is applied to four real and right censored data sets. A new distribution is compared with many other competitive distributions under the new modified Bagdonavičius-Nikulin goodness-of-fit test statistic.

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.

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