We discuss the existence and characterization of quasi-stationary distributions and Yaglom limits of self-similar Markov processes that reach 0 in finite time. By Yaglom limit, we mean the existence of a deterministic function g and a non-trivial probability measure ν such that the process rescaled by g and conditioned on non-extinction converges in distribution towards ν. If the study of quasi...

We consider the maximum waiting time among the first n customers in the GI/G/1 queue. We use strong approximations to prove, under regularity conditions, convergence of the normalized maximum wait to the Gumbel extreme-value distribution when the traffic intensity p approaches 1 from below and n approaches infinity at a suitable rate. The normalization depends on the interarrival-time and servi...

Abstract Extreme waves are an important factor in coastal structures both offshore and onshore structure design. However, due to the difficulty of measuring ocean waves, many areas still do not have measured wave height data. Data processing is required transform wind data into wind-wave value order solve this issue. This study aims analyze extreme based on from BMKG Panjang Radin Inten II stat...

This paper tries to represent a new method for computing the reliability of a system which is arranged in series or parallel model. In this method we estimate life distribution function of whole structure using the asymptotic Extreme Value (EV) distribution of Type I, or Gumbel theory. We use EV distribution in minimal mode, for estimate the life distribution function of series structure and ma...

A modified version of the Kolmogorov-Smirnov (KS) test is presented as a tool to assess whether a specified, although arbitrary, probability model is unsuitable to describe the underlying distribution of a set of observations. The KS test computes distances between points of the sample cumulative distribution function and the hypothetical one as absolute differences between them, and then consi...

We consider an expression for the probability R=P(Y<X) where random variables X and Y denote strength stress, respectively. Our aim is to study effect of dependency between on R. assume that follow exponential distributions their modeled by a copula with parameter theta. obtain closed-form R Farlie-Gumbel-Morgenstern (FGM), Ali-Mikhail-Haq (AMH), Gumbel's bivariate copulas compute Gumbel-Hou...

The real Ginibre ensemble refers to the family of n × n matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately scaled spectral radius converges in law to a Gumbel distribution as n→∞. This fact has been known to hold in the complex and quaternion analogues of the ensemble for some time, with simpler proofs...