Statistical method. If the statistical method (see 23.6) is used, the Manufacturer agreed with the CAB to define Sample: Accepted Quality Level (AQL):
Statistical method. If the statistical method (see 25.7) is used, the Manufacturer agreed with IMCI to define Sample: Accepted Quality Level (AQL):
Statistical method. Suppose that each of N subjects is classified into one of the two categories by each of the same set of ij1 ij2 ij1 ij2 n raters under conditions A and B. Let the random vectors Xa = (Xa , Xa )T and Xb = (Xb , Xb )T represent the resulting classification of the i-th subject (i = 1,..., N) by the j-th rater ( j = 1,..., n) ijc ijc
Statistical method. Our work focuses on trends in heavy daily precipitation totals. Since heavy weather events are, by definition, rare events, they are more difficult to study than averages and robust conclusions about their statistics and changes cannot be drawn from empiric values. Instead, adequate probability distributions which focus in particular on the rare heavy events have to be fitted to the data. To tackle the problem of estimating the distribution of rare events, special statistical rules apply, which are described by extreme value theory. In the present work we make use of a non-homogeneous Poisson point process approach, which is based on a peaks-over-threshold model. The statistical model is fitted to the occurrence of exceedances over a high threshold (i.e. heavy precipitation events in the context here) and the intensity of the excesses over the threshold. The threshold used in this study is the empiric value of the 95th percentile, i.e. the data value which is exceeded by 5% of the rest of the data. A major advantage of the Poisson point process method is that time-dependent parameters can easily be established. This fact makes the approach very useful for the investigation of trends in heavy precipitation events. A more detailed description of the Poisson point process and extreme value statistics in general can be found e.g. in Coles, 2001. From the estimated parameters of the extreme value distribution of daily precipitation events one can finally calculate trends of high percentiles of the distribution, i.e. return values of events with a certain return period. In this study we analyse the trend of the 99th percentile of daily precipitation totals. The 99th percentile of the extreme value distribution refers to an event which occurs once in 100 days. Since we carry out the analysis for winter and summer separately, this is about once per season. Therefore, the trend of the 99th percentile gives an idea how heavy precipitation events with a one-seasonal return period might change in the future. This includes both the frequency and the intensity of heavy precipitation events. To further investigate how the frequency of the events is changing, 30-year running mean values are obtained from the number of the exceedances over the threshold over the whole time period and their linear trends are determined.
