A Simple Algorithm for Generating a New Two Sample Type-II Progressive Censoring with Applications

In this article, we introduce a simple algorithm to generating a new type-II progressive censoring scheme for two samples. It is observed that the proposed algorithm can be applied for any continues probability distribution. Moreover, the description model and necessary assumptions are discussed. In addition, the steps of simple generation algorithm along with programming steps are also constructed on real example. The inference of two Weibull Frechet populations are discussed under the proposed algorithm. Both classical and Bayesian inferential approaches of the distribution parameters are discussed. Furthermore, approximate confidence intervals are constructed based on the asymptotic distribution of the maximum likelihood estimators. Also, we apply four methods of Bootstrap to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are evaluated by applying the Markov chain Monte Carlo technique and credible intervals are also carried out. The Bayes inference based on the squared error and LINEX loss functions is obtained. Simulation results have been implemented to obtain the accuracy of the estimators. Finally, one real data set has been analyzed for illustrative purposes both the proposed algorithm and methods of estimation

The Effects of Evolutionary Adaptations on Spreading Processes in Complex Networks

A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution. However, in real-life spreading processes, pathogens often evolve in response to changing environments and medical interventions and information is often modified by individuals before being forwarded. In this paper, we investigate the evolution of spreading processes on complex networks with the aim of i) revealing the role of evolution on the threshold, probability, and final size of epidemics; and ii) exploring the interplay between the structural properties of the network and the dynamics of evolution. In particular, we develop a mathematical theory that accurately predicts the epidemic threshold and the expected epidemic size as functions of the characteristics of the spreading process, the evolutionary dynamics of the pathogen, and the structure of the underlying contact network. In addition to the mathematical theory, we perform extensive simulations on random and real-world contact networks to verify our theory and reveal the significant shortcomings of the classical mathematical models that do not capture evolution. Our results reveal that the classical, single-type bond-percolation models may accurately predict the threshold and final size of epidemics, but their predictions on the probability of emergence are inaccurate on both random and real-world networks. This inaccuracy sheds the light on a fundamental disconnect between the classical bond-percolation models and real-life spreading processes that entail evolution. Finally, we consider the case when co-infection is possible and show that co-infection could lead the order of phase transition to change from second-order to first-order.Comment: Submitte