## 1 Introduction
In [34], an air conditioner on/off state prediction model, combined with the diversity of occupant behavior, was established. In [35], Lasso regression was used to estimate the consumption of electrical appliances, electric heating, cooling and lighting of building parks in Wallonia. In [36], a Pecan Street dataset was used to group building occupants according to the energy they consume per electro-domestic appliance in their home with a subsequent load profile development. In [37], air-conditioning usage patterns of three climate zones were analyzed and developed. In [38], a thermal model was developed to calculate the regulating power provided by air conditioners. In [39], an optimal load control strategy for air conditioners was proposed. In [40], a model was established to characterize the Spanish electricity consumption considering typical appliances and key parameters of vulnerable households. In [41], a model of commonly used household appliances was constructed and a user satisfaction evaluation index was established. In [42], it was proposed to find the optimal delay time in the most energy-consuming equipment according to the priority of each appliance. All of the above methodologies lack a descriptive statistical analysis of each household appliance for each hour of the day. As alternatives to the previous solutions, this paper proposes an evaluation of the statistical distributions followed by each household appliance in a house [43] and, using them, to generate random values in such a way that they are as close as possible to the real values measured. To check the applicability of the assessment, it has been compared with an average of sets of simulated values with the sets of measured values and, thus, proves that the result is accurate. All the above papers provide different forms of modeling, but none of them deal with the statistical distributions that may follow the consumptions at each period in depth. As a novelty, in this paper, the aim is to discover what statistical distribution the consumption of household appliances follows in 10-min periods, from the most basic ones (such as the normal, exponential or Weibull distribution) to the less known ones (Rayleigh or Generalized Pareto), applying the Kolmogorov-Smirnov test and the X\({}^{2}\) test. To guarantee a correct evaluation, the averages of sets of random values are compared with the averages of real values for each hour, checking that the difference between them is acceptable. Obtaining the statistical distribution of the power consumption of household appliances can be of certain interest because: it avoids dealing with errors, the absence of data or out-of-scale values; it may simulate data corresponding to one, three or even ten years in order to assess all possible scenarios; it can be statistically combined with other models in order to obtain more complex theoretical developments and, last but not least, derived results may be obtained from the type of distribution and its parameters (mean, mode, variance, quantiles, etc.). This article is organized as follows: Section 2 describes the methodology applied for the two different types of consumption to deal with, i.e., the mathematical models and procedures used to obtain the results. Section 3 includes the information of the case study in detail. Section 4 presents the results after applying the methodology, together with a discussion of the results. Finally, Section 5 presents the conclusions of the work carried out.