Probabilities for p-outside values - Particular cases

Abstract

The paper investigates probabilities for p-outside values. It shows that they are very appropriate new numerical characteristics for describing the tail of the cumulative distribution function of the corresponding random variable. They are invariant within the whole probabilistic type. They always exist. They outperform the role of the excess, and have more general applications than the index of regular variation. Their theoretical values in many particular cases, e.g. Pareto, Stable, Gamma, Log-Logistic, Frechet, some p-max-stable laws among others are calculated, and corresponding functions are plotted and compared. These characteristics allow us to find estimators of the tail of the distribution outside the range of the data. Therefore they can be useful in analyzing high quantiles and extremal values.The paper investigates probabilities for p-outside values. It shows that they are very appropriate new numerical characteristics for describing the tail of the cumulative distribution function of the corresponding random variable. They are invariant within the whole probabilistic type. They always exist. They outperform the role of the excess, and have more general applications than the index of regular variation. Their theoretical values in many particular cases, e.g. Pareto, Stable, Gamma, Log-Logistic, Frechet, some p-max-stable laws among others are calculated, and corresponding functions are plotted and compared. These characteristics allow us to find estimators of the tail of the distribution outside the range of the data. Therefore they can be useful in analyzing high quantiles and extremal values.