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The purpose of this paper is to investigate the properties of the classical goodness of fit test statistics X², G², GM², and NM² in testing quality of process represented as the trinomial distribution with dip null hypothesis and to devise a control chart for the trinomial distribution with dip null hypothesis based on demerit control chart.

The research involves the linear form of the test statistics, the linear function of counts since the marginal distribution of the counts in any category is binomial or approximated Poisson, in which the uniformly minimum variance unbiased estimator is the linear function of counts. A control chart is used for monitoring student characteristics in Thailand. The control chart statistics based on an average of the demerit value computed for each student as a weighted average lead to a uniformly most powerful unbiased test marginally. The two‐sided control limits were obtained using percentile estimates of the empirical distribution of the averages of the demerit.

The demerit control chart of the weight set (1, 25, 50) shows a generally good performance, robust to direction of out‐of‐control, mostly outperforms the GM² and is recommended. The X², NM² are not recommended in view of inconsistency and bias. The performance of the demerit control chart of the weight set (1, 25, 50) does not dramatically change between both directions.

None of the multivariate control charts for counts presented in the literature deals with trinomial distribution representing the practical index of the quality of the production/process in which the classification of production outputs into three categories of “good”, “defective”, and “reworked” is common. The demerit‐based control chart presented here can be applied directly to this situation.

The research considers how to deal with the trinomial distribution with dip null hypothesis which no research study so far has presented. The study shows that the classical Pearson's X², Loglikelihood, modified Loglikelihood, and Neyman modified X² could fail to detect an “out‐of‐control”. This research provides an alternative control chart methodology based on demerit value with recommended weight set (1, 25, 50) for use in general.

The purpose of this paper is to propose a new method based on goodness of fit tests for shift detection problems.

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.

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.

To the best of author’s knowledge, no attention has previously been paid to application of goodness of fit tests in process control.

There has been growing interest in recent years in modelling various poverty‐related issues. However, there have not been many attempts at empirical estimation of best‐fit income distribution functions with an objective of subsequent use in poverty focused models. The purpose of this paper is to fill this gap by empirically estimating best‐fit income distribution functions for different household income groups and computing poverty and inequality indices for Sri Lanka.

The authors empirically estimated a number of popular distribution functions found in the income distribution literature to find the best‐fit income distribution using household income and expenditure survey data for Sri Lanka and subsequently estimated various poverty and inequality measures.

The results show that the income distributions of all low‐income household groups follow the beta general probability distribution. The poverty measures derived using these distributions show that among the different income groups, the estate low‐income group has the highest incidence of poverty, followed by the rural low‐income group.

According to the best of the authors' knowledge, empirical estimation of income distribution functions for South Asia has never been attempted. The results of this study, even though based on Sri Lankan data, will be relevant to most developing countries in South Asia and will be very useful in developing poverty alleviation strategies.

This study aims to apply a systematic statistical approach, including several plot indexes, to diagnose the goodness of fit of a logistic regression model, and then to detect the outliers and influential observations of the data from experimental data.

The proposed statistical approach is applied to analyze some experimental data on internal solitary wave propagation.

A suitable logistic regression model in which the relationship between the response variable and the explanatory variables is found. The problem of multicollinearity is tested. It was found that certain observations would not have the problem of multicollinearity. The P‐values for both the Pearson and deviance χ² tests are greater than 0.05. However, the Pearson χ² value is larger than the degrees of freedom. This finding indicates that although this model fits the data, it has a slight overdispersion. After three outliers and influential observations (cases 11, 27, and 49) are removed from the data, and the remaining observations are refitted the goodness‐of‐fit of the revised model to the data is improved.

A comparison of the four predictive powers: R², max‐rescaled R², the Somers' D, and the concordance index c, shows that the revised model has better predictive abilities than the original model.

The goodness‐of‐fit and prediction ability of the revised logistic regression model are more appropriate than those of the original model.

The purpose of this chapter is to provide researchers a summary of some of the latest developments in item response theory (IRT), and to help these groups realize that psychometric tools can now be used for theory testing in addition to the traditional role of improving construct measurement. The author first reviews some of the fundamental tenets of classical test theory to contrast with IRT. He then describes recent advances in goodness-of-fit tests that have helped turn IRT into a model-testing tool. Finally, the author reviews several new test models that provide new flexibilities, summarizing summarize several examples of research that has used these new models in organizational research. At the end of this review, the author provides suggestions to help researchers better use these new IRT tools. Although there have been significant advances in IRT in the past decade, there has not been a systematic review of these developments. This review places those developments in context to provide readers a real appreciation of these breakthroughs.

The purpose of this paper is to provide an analysis of the dependence structure between returns from real estate investment trusts (REITS) and a stock market index. Further, the aim is to illustrate how copula approaches can be applied to model the complex dependence structure between the assets and for risk measurement of a portfolio containing investments in REIT and equity indices.

The usually suggested multivariate normal or variance‐ covariance approach is applied, as well as various copula models in order to investigate the dependence structure between returns of Australian REITS and the Australian stock market. Different models including the Gaussian, Student t, Clayton and Gumbel copula are estimated and goodness‐of‐fit tests are conducted. For the return series, both the Gaussian and a non‐parametric estimate of the distribution is applied. A risk analysis is provided based on Monte Carlo simulations for the different models. The value‐at‐risk measure is also applied for quantification of the risks for a portfolio combining investments in real estate and stock markets.

The findings suggest that the multivariate normal model is not appropriate to measure the complex dependence structure between the returns of the two asset classes. Instead, a model using non‐parametric estimates for the return series in combination with a Student t copula is clearly more suitable. It further illustrates that the usually applied variance‐covariance approach leads to a significant underestimation of the actual risk for a portfolio consisting of investments in REITS and equity indices. The nature of risk is better captured by the suggested copula models.

To the authors', knowledge, this is one of the first studies to apply and test different copula models in real estate markets. Results help international investors and portfolio managers to deepen their understanding of the dependence structure between returns from real estate and equity markets. Additionally, the results should be helpful for implementation of a more adequate risk management for portfolios containing investments in both REITS and equity indices.

The purpose of this paper is to know whether the authors’ productivity pattern of library and information science (LIS) open access journals adheres to Lotka’s inverse square law of scientific productivity. Since the law was introduced, it has been tested in various fields of knowledge, and results have varied. This study has closely followed Lotka’s inverse square law in the field of LIS open access journals to find a factual result and set a baseline for future studies on author productivity of LIS open access journals.

The publication data of selected ten LIS open access journals pertain to authorship, citations were downloaded from the Scopus database and analysed using bibliometric indicators like authorship pattern, collaborative index (CI), degree of collaboration (DC), collaborative coefficient (CC) and citation counts. This study has applied Lotka’s inverse square law to assess authors’ productivity pattern of LIS open access journals and further Kolmogorov-Smirnov (K-S) goodness-of-fit test applied for testing of observed and expected author productivity data.

Inferences were drawn for the set objectives on authorship pattern, collaboration trend and authors’ productivity pattern of LIS open access journals covered in this study. The single authorship pattern is dominant in LIS open access journals covered in this study. The CI, DC and CC are found to be 1.95, 0.47 and 0.29, respectively. The expected values as per Lotka’s law (n = −2) significantly vary from the observed values as per the chi-square test and K-S goodness-of-fit test. Hence, this study does not adhere to Lotka’s inverse square law of scientific productivity.

Researchers may find an idea about the authors’ productivity patterns of LIS open access journals. This study has used the K-S goodness-of-fit test and the chi-square test to validate the authors’ productivity data. The inferences found out from this study will be a baseline for future research on author productivity of LIS open access journals.

This study is significant from the viewpoint of the growing research on open access journals in the field of LIS and to identify the authorship pattern, collaboration trend and author productivity pattern of such journals.

Goodness‐of‐fit test based on K_ϕ‐divergence between observed and theoretical frequencies are considered. The asymptotic chi‐square null distribution and three alternative approximations to the exact distribution function of this family are compared in small samples. Numerical results are presented for the symmetric null hypothesis for different multinomial sample sizes with various cell numbers. Exact power under specific alternatives to the symmetric null hypothesis are calculated and a comparison with the family of power divergence statistics is made.

Purpose – In this chapter, copula theory is used to model dependence structure between hedge fund returns series.

Methodology/approach – Goodness-of-fit tests, based on the Kendall's functions, are applied as selection criteria of the “best” copula. After estimating the parametric copula that best fits the used data, we apply previous results to construct the cumulative distribution functions of the equally weighted portfolios.

Findings – The empirical validation shows that copula clearly allows better estimation of portfolio returns including hedge funds. The three studied portfolios reject the assumption of multivariate normality of returns. The chosen structure is often of Student type when only indices are considered. In the case of portfolios composed by only hedge funds, the dependence structure is of Franck type.

Originality/value of the chapter – Introducing goodness-of-fit bootstrap method to validate the choice of the best structure of dependence is relevant for hedge fund portfolios. Copulas would be introduced to provide better estimations of performance measures.