Many plotting position formulae have been proposed for the past few decades. These formulae are derived or obtained under some speci®c assumption of probability distribution. Because in practice the data are often plotted in order to determine its probability distribution, it causes dif®culty and confusion in selecting the plotting position formula. The objective of this study is to ®nd a plotting position formula which is distribution free. In this study, the plotting position formulae corresponding to the order statistic mean, mode and median are investigated. The order statistic mean, mode and median values are determined by numerical integration and differentiation, and the corresponding plotting position formulae are obtained by regression analysis. The results indicate that both the plotting position formulae for the order statistic mean and mode vary with the distribution of data, but the plotting position formula for the order statistic median is distribution free. The distribution free plotting position formula for the order statistic median is proposed in this study as i À 0:326=n 0:348.
In time series modelling, subset models are often desirable, especially when the data exhibit some form of periodic behaviour with a range of different natural periods in terms of days, weeks, months and years. Recently, Hokstad proposed a method based on personal judgement for selecting the first tentative model to obtain the best subset autoregressive model. The subjective approach adopted in the Hokstad method is a disadvantage in building up a computer program which could automatically select the appropriate model of a given time series. In this paper, we propose overcoming this disadvantage by employing the inverse autocorrelation function to select the first tentative model. In addition to sets of synthetic data, some well-known real series such as the D, E and F series of Box and Jenkins and the Canadian lynx data are analysed to validate the proposed method. The results indicate that the method can successfully detect the true model for a given time series.
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