Risk Analysis Method by the Extreme Data of Dependent Exogenous Variables

Many practical tasks of data multivariate statistical analysis from the standpoint of a risk-oriented process approach (in accordance with ISO 9001: 2015, 31000: 2018) requires the definition of the risk values for the dependent exogenous variables of some processes. This paper proposes the method, which consist of original stages sequence for calculating value-at-risk (VaR) or conditional-value-at-risk (CVaR) of dependent exogenous variables, presented of the extreme data frame of critical manufacture process parameters or other parameters, for example, extreme data of environmental monitoring and etc. Risk analysis method by the extreme data of dependent exogenous variables, presented of the data matrix, uses the result of solving the formalized problem of defines the tails parameters of the joint distributions of exogenous variables as components of a bivariate random variable. It can be argued that the tails parameters of the joint distributions of dependent exogenous variables make the validated corrections of the VaR and CVaR estimates for such variables. This method expands the practical application of extreme value theory for the value at risk analysis of any dependent variables as process parameters.