## 1 Introduction
With regards to the second question and working with methods based on the normality assumption, the non-normality of the data can have various consequences depending on the degree of non-normality of the data and the robustness of the method applied. In this case, the non-normality violates a basic assumption of the method, and this violation is important from a strict perspective. For instance, the minimum quadratic estimators are not efficient, and the confidence intervals and hypothesis tests of parameters can only be approximated. Although it is possible that the results of a method can be considered valid if the non-normality is slight, the results may be completely incorrect if the non-normality is significant [20]. As an example of the above, if the error data contain a few outliers, their elimination from the analysis to achieve normality can give an acceptable result, but if the number of outliers is very large, this elimination is no longer possible. Finally, to answer the third question, it is necessary to consider two very different situations: (a) data are not normally distributed but are distributed following another parametric distribution function (e.g., Weibull, Gamma, etc. ), (b) data do not follow a distribution. In both cases, methods based on normal data are inadequate, but if a parametric distribution can be applied, the properties and parameters of such a distribution can help us work with these data. If the data are freely distributed, an observed distribution function is required for the analysis. Working with observed distributions is more complicated than working with parametric models, but this circumstance does not prevent estimation and decision-making (quality control) within a probabilistic framework [21]. Positional accuracy assessment methods based on free-distributed data are scarce. Following the analysis of [PERSON] & [PERSON] [22], the National Map Accuracy Standard [23] can be considered a method with capabilities to work with free-distributed data. In addition, it is possible to use percentiles when working with this type of error data, but the proposals for the use of percentiles, such as that of [PERSON] [14], are merely descriptive, in the statistical sense, and no method for quality control is given. Error counting is the statistical technique that is used to cope with these cases. Following this idea, several methods exist: [PERSON] et al. [24] describe a method that allows the control of building plans; [PERSON] & [PERSON] [25] propose a method for positional accuracy control of line strings; the Spanish standard for positional accuracy control [26] proposes the use of the defect counting method established by the International Standard ISO 2859 [27]. All of these methods are able to work with free-distributed error data but are very limited by the statistical model that is applied (i.e., the binomial distribution function). The objective of this paper is to propose a new and general statistical method for positional accuracy control that can be applied to any kind of data without the need for any underlying statistical hypothesis, e.g., ALS error data, and in general, for any free-distributed error data or non-normally distributed data. The motivation of this work is twofold: to have a method of quality control that is not subject to the need for normal positional errors and, on the other hand, the possibility of controlling the observed error distribution as much as desired.