## 1 Introduction  
Digital topographic data are indispensable for modern modelling needs in many science branches (e.g., environmental planning, forestry, geology, hydrology, climate change, etc.). Airborne Laser Scanner (ALS) systems record terrain elevation, terrain structure lines, buildings, vegetation and, in general, any feature present in the field and that can be detected by its resolution. One type of product of great importance that is derived from ALS are digital terrain models (DTM). DTM generation using only LiDAR data present limitation to simultaneously distinguish complicated terrain situations (e.g., discontinuities and shape ridges), highly fragmented landscapes, and a variety of objects ([1]). The vertical accuracy of LiDAR-derived DTM for uncovered and vegetated areas is assessed in [2]. By means of 193 check-points measured with GNSS-RTK, the mean vertical accuracy reached 0.091 m, while the RMSE was 0.115 m. Related to volume changing (DEM comparison), in [3], the vertical difference of ALS data for vegetated and no vegetated area of a landslide is reported 0.3 and 0.125 m respectively. In the case of the errors caused by the forest vegetation structure, the presence of leaf-on vegetation causes significant errors (RMSE \(>\) 1 m), in contrast with the leaf-off conditions (RMSE = 0.22 m) according to the results presented by [4]. In [5], the influence of factors such as forest structure, slope, off-nadir angle, understory vegetation and filtration and interpolation algorithm on ALS-derived DTM accuracy in mixed mountainous forests was evaluated. The RMSE and the mean error ranged from 0.19 to 0.23 m, and from 0.13 to 0.16 m, respectively, being the slope and the undergrowth vegetation the most important factors influencing DTM accuracy. In [6], as part of a multitemporal study of an alpine rock glacier, the signed discrepancy for stable areas yielded a standard deviation of 0.23 m for a time span of 5 years. LiDAR precision is also evaluated for physical features, as for example in [7], where the LiDAR error for dimensional features of a bridge and several fence posts reach up to 23.5%. The best way to assess or control positional accuracy is by applying standardized methods. Some of them are the National Standard for Spatial Data Accuracy [8], the Engineering Map Accuracy Standard [9], the Standardization Agreement 2215 [10], the Positional Accuracy Standards for Digital Geospatial Data [11] and the European Spatial Data Research (EuroSDR) through its proposal of accuracy measures for digital surface models based on parametric approaches [12]. More precisely, EuroSDR proposes the use of the relative vertical accuracy, the absolute vertical accuracy, and the relation pointed out between them. [PERSON] and [PERSON] [13] presented an analysis of the main features of some of these methods, and in many cases, they are based on the assumption of the normality of the errors. However, many authors [14; 15; 16; 17; 18; 19] indicate that positional errors are not normally distributed. The normal distribution is a suitable distribution for representing real-valued random variables. Therefore, the situation described above regarding positional errors leads to three important questions: (1) why may error data be non-normally distributed? (2) how does non-normality affect the methods based on the assumption of normally distributed data? and finally, (3) how can we work with non-normal data? For the first question, and from a general point of view, six main causes of the non-normality of errors can be considered: (i) the presence of too many extreme values (i.e., outliers), (ii) the overlap of two or more processes, (iii) insufficient data discrimination (e.g., round-off errors, poor resolution), (iv) the elimination of data from the sample, (v) the distribution of values close to zero or the natural limit, and (vi) data following a different distribution (e.g., Weibull, Gamma, etc.). Additionally, some of these causes can appear together.