A shape space for generalized beta exponential distributions of the second type

The generalized beta exponential distribution of the second type contains subfamilies of logistic distributions, that are often used to control time arrays in complex systems. Currently, the choice of a model from possible implementations of a generalized family remains a rather time-consuming task. For this reason, it is often necessary to use complex mixtures of models. Displaying subfamilies of a generalized exponential distribution of the second type in the space of parametric and information features to choose the simplest form of the model from subfamilies and to evaluate the shape parameters is enabled. In the space of standardized moments of the third and fourth order the trajectories position of possible realizations limits the upper limit of distinguish-ability of the shape parameters of distribution models. A significant expansion of the distinguish-ability of trajectories it is possible to achieved by using the entropy coefficient of non-shifted distributions as an additional independent feature of the distribution shape. Mapping subfamilies of distributions in the space of entropy coefficient, antikurtosis and skewness one also to analyse the most important properties of distributions as well is allows. In article it is shows that for all models of the generalized distribution of the second type, the antikurtosis is in the range between the exponential and normal distributions.