In this paper we derive closed-form solutions for the cumulative density function and the average value-at-risk for five subclasses of the infinitely divisible distributions: classical tempered stable distribution, Kim-Rachev distribution, modified tempered stable distribution, normal tempered stable distribution, and rapidly decreasing tempered stable distribution. We present empirical evidenc...

This work demonstrates the attractivity of alpha-skew hyperbolic secant distribution, a new skewed distribution based on technique and distribution. In first part, we determine its main features, including cumulative function, modality, non-central moments, skewness, kurtosis, moment generating function characteristic function. The remaining part is devoted to model applicability in statistical...

We consider the nonparametric kernel estimation of the conditional cumulative distribution function given a functional covariate. Given the bias-variance trade-off of the risk, we first propose a totally data-driven bandwidth selection device in the spirit of the recent Goldenshluger-Lepski method and of model selection tools. The resulting estimator is shown to be adaptive and minimax optimal:...

1. Abstract We propose a reliability analysis (RA) method that obtains the probability of failure by sequentially approximating the cumulative distribution function (CDF). This method uses the concept of the first order reliability method (FORM) in estimating the probability of failure but does not solve the optimization problem to obtain the most probable point (MPP). The goal of the proposed ...

Using the limit theorem for stochastic integral obtained by Jakubowski et al. (Probab. Theory Related Fields 81 (1989) 111–137), we introduce in this paper a new method for proving weak convergence results of empirical processes by a martingale method which allows discontinuities for the underlying distribution. This is applied to Nelson–Aalen and Kaplan–Meier processes. We also prove that the ...

In this paper correspondence between experimental data for packet delay and two theoretical types of distribution is investigated. Statistical tests have shown that only exponential distribution can be used for the description of packet delays in global network. Precision experimental data to within microseconds are gathered by means of the RIPE Test Box. Statistical verification of hypothesis ...