The general approach to modeling binary data for the purpose of estimating the propagation of an internal solitary wave (ISW) is based on the maximum likelihood estimate (MLE) method. In cases where the number of observations in the data is small, any inferences made based on the asymptotic distribution of changes in the deviance may be unreliable for binary data (the model's lack of fit is described in terms of a quantity known as the deviance). The deviance for the binary data is given by D. Collett (2003). may be unreliable for binary data. Logistic regression shows that theP-values for the likelihood ratio test and the score test are both<0.05. However, the null hypothesis is not rejected in the Wald test. The seeming discrepancies inP-values obtained between the Wald test and the other two tests are a sign that the large-sample approximation is not stable. We find that the parameters and the odds ratio estimates obtained via conditional exact logistic regression are different from those obtained via unconditional asymptotic logistic regression. Using exact results is a good idea when the sample size is small and the approximateP-values are<0.10. Thus in this study exact analysis is more appropriate.

To develop estimators with stronger efficiencies than the trimmed means which use the empirical quantile, Kim (1992) and Chen & Chiang (1996), implicitly or explicitly used the symmetric quantile, and thus introduced new trimmed means for location and linear regression models, respectively. This study further investigates the properties of the symmetric quantile and extends its application in several aspects. (a) The symmetric quantile is more efficient than the empirical quantiles in asymptotic variances when quantile percentage α is either small or large. This reveals that for any proposal involving the α th quantile of small or large α s, the symmetric quantile is the right choice; (b) a trimmed mean based on it has asymptotic variance achieving a Cramer-Rao lower bound in one heavy tail distribution; (c) an improvement of the quantiles-based control chart by Grimshaw & Alt (1997) is discussed; (d) Monte Carlo simulations of two new scale estimators based on symmetric quantiles also support this new quantile.Regression quantile, scale estimator, trimmed mean,

PurposeThis 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.Design/methodology/approachThe proposed statistical approach is applied to analyze some experimental data on internal solitary wave propagation.FindingsA 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.Practical implicationsA 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.Originality/valueThe goodness‐of‐fit and prediction ability of the revised logistic regression model are more appropriate than those of the original model.

Building from the consideration of closeness, we propose the mode quasi-range as an alternative scale parameter. Application of this scale parameter to formulate the population standard deviation is investigated leading to an efficient sample estimator of standard deviation from the point of asymptotic variance. Monte Carlo studies, in terms of finite sample efficiency and robustness of breakdown point, have been performed for the sample mode quasi-range. This study reveals that this closeness consideration-based mode, quasi-range, is satisfactory because these statistical procedures based on it are efficient and are less misleading for drawing conclusion from the sample results.breakdown point, range, robustness, quasi-range, scale parameter,

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