Utilizarea simulării stocastice Monte Carlo pentru determinarea fluctuaţiilor minimului de trai decent într-o populaţie dată - Ştefănescu, Ştefan; Mihăilescu, Adina (Calitatea Vieții, 2012)
By normative method we can evaluate, for example, the minimum income needed for a decent living in a given subpopulation data. The level of w is calculated taking into account various types of expenses. Usually, in the literature, this approach is a so-called determinist one, the expenses being interpreted as constants, which the calculation method will be described below. In reality, the expenses cj fluctuate within certain limits, following various types of distributions, with respect to the assumptions made. In this approach, the level is actually a random variable which distribution we intend to estimate. In the following, we suggest a methodology based on the stochastic Monte Carlo simulation in order to determine the empirical distribution of random w values. There were, thus, proposed several hypotheses concerning the shape of the expenses, cj distribution, as well as the possible relations between these expenses. In fact, the expenditures of the studied population, which is below a given threshold value, show the percentage of the analyzed population which find itself in a poverty situation, or otherwise, “falls into poverty”. For example, 12% of individuals, about the entire first decile (option VI) (Table 3.4), shows that the segment of the population which spends more than 1 850 lei falls into poverty, and at a threshold of 1 882 lei, 25% of individuals, about the first quartile, enters poverty if this threshold is exceeded. The actual value of an indicator is not very often useful in practice, if there isn’t also considered a view upon the variations of the coefficient. Thus, the value of an index once obtained, we will find the estimation using the stochastic simulation Monte Carlo, while respecting the constraints imposed by the problem, and the range of variation of the indicator. This work method was also applied for the case of the normative method of minimum income evaluation, namely, the necessary income for a decent living of a two members family with two children, living in an urban area. W is determined taking into account different types (cj) of expenses. Usually in literature, cj are deterministic, being considered as constants. This approach however, doesn’t takes into account the fluctuations of the expenses, fluctuations which are often specific to a given actual situation. This new approach states that w was not a determinist constant, being rather a fluctuating variable w which statistical characteristics are estimated. We suggested here a method based on the statistical simulation Monte Carlo, with the intention to finally determine (establish) the empirical repartition of w values. Thus, several work variants were proposed with respect to the statistical repartition of cj expenses (SV1 and SV2 politics), being, at the same time, possible to impose some sort of interdependence among the types of expenses. The statistical simulation used for the evaluation of the decent minimum standard of living implied specific work hypotheses. Once we established the SMC algorithm Monte Carlo, the implemented constraints could be modified. In this respect, we suggest the following amendments: – the random variables A–J are not necessary independent, being emphasized different relations of dependence; – the marginal repartitions of cj expenses are not compulsory (obligatory) of triangular type, many other types of repartition being possible to be used; – the variation limits of expenses cj will be modified following an actual (real) situation; – we shall not impose in a compulsory manner that all the repartitions of fluctuation variables A–J to be symmetrical, the fluctuation of expenses being rather asymmetrical in real life; – based on the experimental data, various estimation methods will be analyzed (parametric and nonparametric) to establish the statistical characteristics of the proposed models variables (the estimation of parameters α characterizing the density of distribution of the input variables in the system S). – a much more sophisticated approach is the statistical simulation of consume in households, because (as) households are interconnected in a social net with different types of interactions. We intentionally avoided to present technical details of the actual ways of computer generation of the fluctuating variables which follow, for example, a triangular repartition g. In conclusion, the proposed Monte Carlo simulation method helps us to predict the fluctuation of the values of W index which defines the decent minimum standard of living, when keeping its average value, and fluctuating perturbations of a specific intensity intervene within the index’s components.