## 1 Introduction  
The determination measurement's uncertainty made with coordinates measuring machines (CMMs) is an important line of research in the field of coordinate metrology [1; 2]. Although there are different papers [3; 4] in which the uncertainty calculation is based on GUM approach [5], this model is impractical for most situations that appear in the field of coordinate metrology, since the GUM approach does not provide a solution to the singularities that arise, for example,  
* multi-dimensional models based on the coordinates of multiple points;
* the impossibility of determining the sensitivity coefficients of some parameters when these are the result of the application of filters, adjustment algorithms, etc. ;
* the existence of input variables of the model that have non-symmetric distributions;
* the nonlinearity of calculation models that force one to consider higher-order terms. [PERSON] et al. [6] conducted a comprehensive analysis of the various models for calculating. To avoid these problems, different authors have proposed different methods. [PERSON] et al. [6] used a numerical method for calculating uncertainties associated with specific measurement tasks, due to the complexity of the measures. They analysed the concept of \"_virtual CMM_\", which materialises a very precise mathematical model of behavior of a CMM. This model simulates data acquisition, measurement strategy, and physical behavior of the CMM. By the later use of the Monte Carlo method, it is possible to determine the measurement uncertainty. [PERSON] et al. [7] proposed a method for the evaluation of the uncertainty associated with measurements made by a CMM from information obtained after checking the machine using the ISO 10360-2 [8]. The Monte Carlo method [9] is the appropriate solution to estimate the uncertainty associated with measurements obtained with equipment based in coordinate metrology and allows solving problems such as:* arbitrarily complicated models or input quantities of the model present asymmetrical probability density functions (PDF). According to Supplements 1 and 2 to the GUM [9; 10], the steps to be followed to use the Monte Carlo method are as follows:
* formulation, in which the following is defined: (1) the output quantities of model (measurand), (2) the input quantities of the model, (3) the measurement model that connects the inputs with the outputs, (4) the assignment of PDF to each input quantity;
* the propagation of the PDF assigned to the input quantities using the measurement model, obtaining the PDF of each output quantity; and
* a summary determining for each output quantity, from its PDF, their mathematical expectation, standard uncertainty, uncertainty coverage interval, and covariance matrix. It is possible to find metrological models that provide correlated output quantities with PDF not comparable to any known. When these quantities are used in subsequent calculation measurement models, the propagation of these quantities cannot use the procedures described in Supplements 1 and 2 of the GUM. In these cases, the theory of copulas is often used [11; 12; 13; 14], which develops functions capable of describing dependencies between variables and providing multivariate data that model correlated distributions. The use of the theory of copulas has disadvantages such as high computation times and complexity of the developed algorithms, disadvantages that in an industrial environment are critical parameters. The aim of this paper is to analyse the effect of various hypotheses about the type of the input quantities distributions of the measurement model so that the developed algorithms can be simplified.