Shannon and Rényi entropies are two important measures of uncertainty for data analysis. These have been studied multivariate Student-t skew-normal distributions. In this paper, we extend the entropy to skew-t finite mixture (FMST) This class flexible distributions allows handling asymmetry tail weight behavior simultaneously. We find upper lower bounds these families. Numerical simulations ill...

ii I certify that I have read this dissertation and certify that in my opinion it is fully adequate, in scope and in quality, as a dissertation for the degree of Doctor of Philosophy. Stochastic dependence arises in many fields including electrical grid reliability, net-work/internet traffic analysis, environmental and agricultural impact assessment, and financial risk management. Models in the...

Global-local shrinkage hierarchies are an important, recent innovation in Bayesian estimation of regression models. In this paper we propose to use log-scale distributions as a basis for generating familes of flexible prior distributions for the local shrinkage hyperparameters within such hierarchies. An important property of the log-scale priors is that by varying the scale parameter one may v...

In this paper, we provide (i) a rigorous general theory to elicit conditions on (tail-dependent) heavy-tailed cyber-risk distributions under which risk management firm might find it (non)sustainable aggregate coverage services for smart societies, and (ii)a real-data driven numerical study validate claims made in assuming boundedly rational managers, alongside providing ideas boost markets that...

A new method to estimate longevity risk based on the kernel estimation of extreme quantiles truncated age-at-death distributions is proposed. Its theoretical properties are presented and a simulation study reported. The flexible yet accurate conditional having survived certain age fundamental for evaluating lifetime insurance. Our proposal combines parametric with nonparametric sample informati...

We consider the cyclic polling system with two queues. One queue is served according to the exhaustive discipline, and the other queue is served according to the 1-limited discipline. At least one of the service and/or switchover times has a regularly varying tail. We obtain the tail behavior of the waiting time distributions. When one of the service and/or switchover times has an infinite seco...

For some computing systems failure is rare enough that it can be ignored. In others, failure is common and software design considerations can have a significant impact upon the performance of applications running on the systems. In this paper, we discuss software design issues that should be considered whenever jobs execute in unreliable computing environments. Specifically, we show that if pro...

The 4-parameter generalized lambda distribution (GLD) is a flexible distribution capable of mimicking the shapes of many distributions and data samples including those with heavy tails. The method of L-moments and the recently developed method of trimmed L-moments (TL-moments) are attractive techniques for parameter estimation for heavy-tailed distributions for which the Land TL-moments have be...

This paper deals with estimating small tail probabilities of the steady-state waiting time in a GI/GI/1 queue with heavy-tailed (subexponential) service times. The interarrival times can have any distribution with a nite mean. The problem of estimating in nite horizon ruin probabilities in insurance risk processes with heavy-tailed claims can be transformed into the same framework. It is well-k...