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This study examined performance of the beta-binomial model in comparison with GEE using clustered binary responses resulting in non-normal outcomes. Monte Carlo simulations were performed under varying intracluster correlations and sample sizes. The results showed that the beta-binomial model performed better for small sample, while GEE performed well under large sample.

This paper investigates how unit root tests that are designed for non-normal errors perform in the presence of unknown forms of nonlinearity. This allows us to examine whether any neglected nonline...

We present PLSIM, a new method for generating nonnormal data with a pre-specified covariance matrix that is based on coordinate-wise piecewise linear transformations of standard normal variables. In our presentation, the piecewise linear transforms are chosen to match pre-specified skewness and kurtosis values for each marginal distribution. We demonstrate the flexibility of the new method, and an implementation using R software is provided.

The root mean square error of approximation (RMSEA) with various corrections for non-normality is a common fit index in structural equation modeling (SEM). The present study analyzed the performanc...

The important and common applications of process capability indices (PCI’s) is the process capability ratio and the process capability index , and the use of these measures in practical applications is based on the assumption that the process is under statistical control and that the outputs of that process follow the normal distribution. In practice, however, there are many cases in which the outputs of the process are not follow normal distribution, in such cases, calculating PCI’s will lead to misleading results. In this paper, the non-normal production process capability was evaluated. The evaluation process was conducted using four methods: The first method involved the use of Box-Cox power transformation to normal distribution of data and then calculating indicators of the capability process by traditional methods. The second method is by using the weighted variance method, and the third method is by using the Clements’ method based on the percentiles calculation of data, and the fourth method is based on the use of the Darling-Anderson goodness of fit test to accommodate some of the probability distributions of the original data, this test shows that the log-normal distribution is the most appropriate distribution for the data The results showed that although the process is stable and under statistical control, it is not capable based on the value of the process capability index that did not exceed (65%), as the percentage defect units, which is outside the specifications, is large and located between (3.6%) and (13.4%). The results also showed that there is a convergence in the results of the PCI’s calculated by all methods, and that the Clements’ method is the best method as it gives the highest values ​​for the PCI’s. The research recommended studying and calculating other PCI’s like, , , and CMA(τ,v). One of the recommendations for future research and studies is to do a theoretical study to compare the mentioned methods and choose the best ones based on some statistical criteria.

The mixed variable discriminant analysis procedure assumes that observations are distributed multivariate normal with different group means but same variance-covariance matrix. However, attention h...

Previous studies suggested that the power of unit root and stationarity tests can be improved by augmenting a testing regression model with stationary covariates. However, one practical problem arises since such procedures require finding the variables that satisfy certain conditions. The difficulty of finding satisfactory covariate has hindered using such desired tests. In this paper, we suggest using non-normal errors to construct stationary covariates in testing for stationarity. We do not need to look for outside variables, but we utilize the distributional information embodied in a time series of interest. The terms driven from the information on non-normal errors can be employed as valid stationary covariates. For this, we adopt the framework of stationarity tests of Jansson (Jansson, M. 2004. “Stationarity Testing with Covariates.” Econometric Theory 20: 56–94). We show that the tests can achieve much-improved power. We then present the response surface function estimates to facilitate computing the critical values and the corresponding p-values. We investigate the nature of shocks to the US macro-economic series using the updated Nelson–Plosser data set through our new testing procedure. We find stronger evidence of non-stationarity than their univariate counterparts that do not use the covariates.

The development and application of the traditional univariate and multivariate quality control charts are distribution-based following the assumption that the process outputs come from some specifi...

In this paper, we call a finite group G G an N L M NLM -group ( N C M NCM -group, respectively) if every non-normal cyclic subgroup of prime order or order 4 (prime power order, respectively) in G G is contained in a non-normal maximal subgroup of G G . Using the property of N L M NLM -groups and N C M NCM -groups, we give a new necessary and sufficient condition for G G to be a solvable T T -group (normality is a transitive relation), some sufficient conditions for G G to be supersolvable, and the classification of those groups whose all proper subgroups are N L M NLM -groups.

This paper aims to study the impacts of long memory in conditional volatility and conditional non-normality on market risks in Bitcoin and some other cryptocurrencies using an Autoregressive Fracti...

Let G be a finite p-group. Assume that $$\nu (G)$$ and $$\nu _c(G)$$ denote the number of conjugacy classes of non-normal subgroups and non-normal cyclic subgroups of G, respectively. In this paper, we completely classify the finite p-groups with $$\nu _c=p$$ or $$p+1$$ for an odd prime number p. Also, we classify the groups G with $$\nu (G)=\nu _c(G)=p^i, i\ge 1$$ .

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In this paper, a robust interval estimator for the classical process capability index (Cp) based on the modified trimmed standard deviation (MTSD = ST ∗ ) is considered under both normal and non-normal distributions. The performance of the newly proposed process capability index interval estimator over the existing method is compared using a simulation study. As a performance criterion, we consider both simulated coverage probability and average width. Simulation results evident that the proposed confidence interval based on the robust estimator performed well for most of cases. For illustration purposes, two real-life data from industry are analyzed which supported our simulation results to some extent. As a result, the proposed method can be recommend to be used by the practitioners in various fields of industry, engineering and physical sciences.

Various creative multi-response optimisation approaches have been developed in the literature. Most of these researches are based on the normality assumption of the response distribution. However, ...

Some properties of k-quasi-M-hyponormal are established in this paper. The ascent and an extension of thewell-known Fuglede Putnam's Theorem for such operators as well as other related results are also presented,which complete some results given in [7, 12].

We investigate the influence of some natural types of subgroups on the structure of groups. A subgroup H of a group G is called contranormal in G, if G = H^G. A subgroup H of a group G is called core-free in G, if CoreG(H) = 〈1〉. We study the groups, in which every non-normal subgroup is either contranormal or core-free. In particular, we obtain the structure of some monolithic and non-monolithic groups with this property. Досліджено вплив деяких типів підгруп на структуру груп. Підгрупу H групи G називаємо контранормаль ною в G, якщо G = H^G. Підгрупу H групи G називаємо вільною від ядра в G, якщо CoreG(H) = 〈1〉. Вивчено групи, в яких кожна підгрупа або нормальна, або контранормальна, або вільна від ядра. Точніше, одержано будову деяких монолітичних та немонолітичних груп з цією властивістю.

C. I. Lewis’ systems were the first axiomatisations of modal logics. However some of those systems are non-normal modal logics, since they do not admit a full rule of necessitation, but only a restricted version thereof. We provide G3-style labelled sequent calculi for Lewis’ non-normal propositional systems. The calculi enjoy good structural properties, namely admissibility of structural rules and admissibility of cut. Furthermore they allow for straightforward proofs of admissibility of the restricted versions of the necessitation rule. We establish completeness of the calculi and we discuss also related systems.

A finite group P is said to be primary if |P|=pa for some prime p. We say a primary subgroup P of a finite group G satisfies the Frobenius condition in G if NG(P)/CG(P) is a p-group provided P is p...

The comparison of two samples is a problem very frequently encountered in practice. There is active interest in researching for tests that are powerful also when the data are not compatible with th...

Modern multivariate control charts that use spatial signed rank are sensitive to the detection of small shifts under non-normal or gamma distributions. In this paper, Monte Carlo simulation is used to compare the performances of multivariate control charts based on the average run length. The results show that the spatial signed-rank multivariate exponentially weighted moving average (SSRM) control chart outperforms the multivariate exponentially weighted moving average (MEWMA) control chart, the double-MEWMA control chart, and the spatial signed-rank double multivariate exponentially weighted moving average control chart when detecting small shifts in the process mean. SSRM is appropriate for data from a non-normal distribution, which is valuable for the manufacturing industry when detecting waste. Moreover, SSRM is an excellent method suitable for most industrial processes, and therefore, is a very powerful tool.

A simulation study was conducted to examine the efficacy of nine frequently-used HOV tests, including Levene’s tests with squared residuals and with absolute residuals, Brown and Forsythe (BF) test...

Although the Analysis of Variance (ANOVA) F test is one of the most popular statistical tools to compare group means, it is sensitive to violations of the homogeneity of variance (HOV) assumption. This simulation study examines the performance of thirteen tests in one-factor ANOVA models in terms of their Type I error rate and statistical power under numerous (82,080) conditions. The results show that when HOV was satisfied, the ANOVA F or the Brown-Forsythe test outperformed the other methods in terms of both Type I error control and statistical power even under non-normality. When HOV was violated, the Structured Means Modeling (SMM) with Bartlett or SMM with Maximum Likelihood was strongly recommended for the omnibus test of group mean equality.

The Pacific–North American (PNA) teleconnection pattern has been linked both to tropical phenomena, including the Madden–Julian oscillation (MJO) and El Niño–Southern Oscillation (ENSO), and to internal extratropical processes, including interactions with the zonally varying basic state and synoptic eddies. Many questions remain, however, concerning how these various relationships act, both separately and together, to yield observed PNA variability. Using linear inverse modeling (LIM), this study finds that the development and amplification of PNA anomalies largely results from the interference of modes strongly coupled to sea surface temperatures (SST), such as ENSO, and modes internal to the atmosphere, including the MJO. These SST-coupled and “internal atmospheric” modes form subspaces that are not orthogonal, and PNA growth is shown to occur via non-normal interactions. An internal atmospheric space LIM is developed to examine growth beyond this interference by removing the SST-coupled modes, effectively removing ENSO and retaining MJO variability. Optimal PNA growth in the internal atmospheric space LIM is driven by MJO heating, particularly over the Indian Ocean, and a retrograding northeast Pacific streamfunction anomaly. Additionally, the individual contributions of tropical heating and the extratropical circulation on PNA growth are investigated. The non-normal PNA growth is an important result, demonstrating the difficulty in partitioning PNA variance into contributions from different phenomena. This cautionary result is likely applicable to many geophysical phenomena and should be considered in attribution studies.

In the last decades, the availability of attitudinal surveys generating data of ordinal (discrete) nature has increasingly risen. Such kind of data may be also associated with responses expressed t...

Normality of latent traits is a common assumption made when estimating parameters for item response theory (IRT) models, but this assumption may be violated. The purpose of this research was to present a new Markov chain Monte Carlo (MCMC) method for ordinal items with flexible latent trait distributions (i.e., skewed and bimodal). Specifically, the Davidian curve (DC) was used to approximate the distribution of latent traits. The performance of the proposed MCMC algorithm with DCs was evaluated via a simulation study and compared with an EM method using DCs that is available in the "mirt" package (Chalmers, 2012). The manipulated factors included the number of response categories, sample size, and the shape of the latent trait distribution. The Hanna-Quinn (HQ) criterion was used to choose the best DC order. Results indicated that when informative priors were used, the MCMC algorithm with DCs could fit a flexible distribution well and the method provided good parameter estimates which, under some circumstances, had lower bias and RMSE than the EM method.

It has been usually assumed that a sample data is normally distributed when the sample size is at least 30. This is the general rule in using central limit theorem based on the sample size being greater or equal to 30. Many literary works also assumed normality when sample size is at least 30. This study aims to determine the least required sample size that satisfy normality assumption from three non-normal distributions, Poisson, Gamma and Exponential distributions. Computer simulations are carried out to study the least required sample size for the three distributions. Through the study, it is found that sample data from Poisson and Gamma distributions need sample size less than 30, while Exponential needs more than 30 to achieve normality.

Capability indices are the most common tools in process capability analysis, measuring how much the product meets the costumer expectations. One type of capability indices are loss-based indices th...

In exploratory factor analysis (EFA), cross-loadings frequently occur in empirical research, but its effects on determining the number of factors to retain are seldom known. In this paper, we analy...

A Cayley graph $$\mathrm{Cay}(G, S)$$ on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of $$\mathrm{Cay}(G, S)$$ . In this paper, a complete classification is given of tetravalent non-normal Cayley graphs of order $$2p^2$$ for each prime p.

Let G be a finite groupand H is a subgroup of G. The subgroup graph of H in G is defined as a directed simple graph with vertex set G and two distinct elements x and y are adjacent if and only if xy∈H. In this paper, the work on subgroup graph is extended by defining a new graph called the non-normal subgroup graph. The subgroup graph is determined for some dihedral groupsof order 2n when the subgroup is non-normal. Keywords: subgroup graph; non-normal subgroup; dihedral group

It is often unrealistic to assume normally distributed latent traits in the measurement of health outcomes. If normality is violated, the item response theory (IRT) models that are used to calibrate questionnaires may yield parameter estimates that are biased. Recently, IRT models were developed for dealing with specific deviations from normality, such as zero-inflation (“excess zeros”) and skewness. However, these models have not yet been evaluated under conditions representative of item bank development for health outcomes, characterized by a large number of polytomous items. A simulation study was performed to compare the bias in parameter estimates of the graded response model (GRM), polytomous extensions of the zero-inflated mixture IRT (ZIM-GRM), and Davidian Curve IRT (DC-GRM). In the case of zero-inflation, the GRM showed high bias overestimating discrimination parameters and yielding estimates of threshold parameters that were too high and too close to one another, while ZIM-GRM showed no bias. In the case of skewness, the GRM and DC-GRM showed little bias with the GRM showing slightly better results. Consequences for the development of health outcome measures are discussed.

Robust parameter design (RPD) is an effective tool, which involves experimental design and strategic modeling to determine the optimal operating conditions of a system. the usual assumptions of RPD are that normally distributed experimental data and no contamination due to outliers. and generally the parameter uncertainties in response models are neglected. However, using normal theory modeling methods for a skewed data and ignoring parameter uncertainties can create a chain of degradation in optimization and production phases such that misleading fit, poor estimated optimal operating conditions, and poor quality products. This article presents a new approach based on confidence interval (CI) response modeling for the process mean. the proposed interval robust design makes the system median unbiased for the mean and uses midpoint of the interval as a measure of location performance response. As an alternative robust estimator for the process variance response modeling, using biweight midvariance is proposed which is both resistant and robust of efficiency where normality is not met. the results further show that the proposed interval robust design gives a robust solution to the skewed structure of the data and to contaminated data. the procedure and its advantages are illustrated using two experimental design studies.

The paper provides five tests of data normality at different sample sizes. The tests are the Shapiro-Wilk (SW) test, Anderson-Darling (AD) test, Kolmogorov-Smirnov (KS) test, Ryan-Joiner (RJ) test, and Jarque-Bera (JB) test. These tests were used to test for normality for two secondary data sets with sample size (155) for large and (40) for small; and then test the simulated scenario with standard normal “N(0,1)” data sets; where the large samples of sizes (150, 140, 130, 130, 110 and 100) and small samples of sizes (40. 35, 30, 25, 20, 15 and 10) are considered at two levels of significance (5% and 10%). However, the aim of this paper is to detect and compare the performance of the different normality tests considered. The normality test results shows Kolmogorov-Smirnov (KS) test is a most powerful test than other tests since it detect the simulated large sample data sets do not follow a normal distribution at 5%, while for small sample sizes at 5% level of significance; the results showed the Jarque-Bera (JB) test is a most powerful test than other tests since it detects that the simulated small sample data do not follow a normal distribution at 5%. This paper recommended JB test for normality test when the sample size is small and KS test when the sample size is large at 5% level of significance.

Prior studies investigating the effects of non-normality in structural equation modeling typically induced non-normality in the indicator variables. This procedure neglects the factor analytic structure of the data, which is defined as the sum of latent variables and errors, so it is unclear whether previous results hold if the source of non-normality is considered. We conducted a Monte Carlo simulation manipulating the underlying multivariate distribution to assess the effect of the source of non-normality (latent, error, and marginal conditions with either multivariate normal or non-normal marginal distributions) on different measures of fit (empirical rejection rates for the likelihood-ratio model test statistic, the root mean square error of approximation, the standardized root mean square residual, and the comparative fit index). We considered different estimation methods (maximum likelihood, generalized least squares, and (un)modified asymptotically distribution-free), sample sizes, and the extent of non-normality in correctly specified and misspecified models to investigate their performance. The results show that all measures of fit were affected by the source of non-normality but with varying patterns for the analyzed estimation methods., publishedVersion