A shape mapping for generalized beta exponential distribution of the first kind in the entropy-parametric space

Abstract

Abstract Modern methods of tracking and controlling complex systems are associated with the analysis of the shape of statistical models of sample arrays. Often the values of the monitored parameters are maintained only on a semi-infinite range of values. In these cases, it is possible to use generalized beta exponential distribution models of the first kind to smooth the statistics, that it is including such models as exponential and generalized Gompertz-Verhulst distributions as special cases. The distributions with a large set of subfamilies rarely are use due to lack of methods of preliminary estimation of the distribution shape parameters. The paper illustrates that the displayed of distributions in the parametric space of skewness and kurtosis does not allow distinguishing the features of the position of the main subfamilies of distributions. Mapping the subfamilies of the Generalized Beta Exponential Distribution of the first kind in the Entropy-Parametric space makes it possible to distinguish between subfamilies and to comparative analysis of many their properties. It is convenient to use the space of the entropy coefficient and skewness when you are comparing the skew properties of distributions. The space of the entropy coefficient and antikurtosis is more suitable for comparing the weights of distribution tails and for analysing monotonicity. In particular, it is shown that the Generalized Beta Exponential Distribution of the first kind contains as monotonic and as non-monotonic leptokurtic distributions. The property of monotonicity is well discernible when compared with the antikurtosis of the exponential distribution.