The Distributions of Stopping Times For Ordinary And Compound Poisson Processes With Non-Linear Boundaries: Applications to Sequential Estimation
نویسنده
چکیده
Distributions of the first-exit times from a region with non-linear upper boundary are discussed for ordinary and compound Poisson processes. Explicit formulae are developed for the case of ordinary Poisson processes. Recursive formulae are given for the compound Poisson case, where the jumps are positive, having continuous distributions with finite means. Applications to sequential point estimation are illustrated.
منابع مشابه
Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes
Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...
متن کاملدربارۀ شناسایی بیزیِ دنبالهای نقطۀ تغییر
The problems of sequential change-point have several important applications in quality control, signal processing, and failure detection in industry and finance and signal detection. We discuss a Bayesian approach in the context of statistical process control: at an unknown time τ, the process behavior changes and the distribution of the data changes from p0 to p1. Two cases are consi...
متن کاملDrift Change Point Estimation in the rate and dependence Parameters of Autocorrelated Poisson Count Processes Using MLE Approach: An Application to IP Counts Data
Change point estimation in the area of statistical process control has received considerable attentions in the recent decades because it helps process engineer to identify and remove assignable causes as quickly as possible. On the other hand, improving in measurement systems and data storage, lead to taking observations very close to each other in time and as a result increasing autocorrelatio...
متن کاملBayesin estimation and prediction whit multiply type-II censored sample of sequential order statistics from one-and-two-parameter exponential distribution
In this article introduce the sequential order statistics. Therefore based on multiply Type-II censored sample of sequential order statistics, Bayesian estimators are derived for the parameters of one- and two- parameter exponential distributions under the assumption that the prior distribution is given by an inverse gamma distribution and the Bayes estimator with respect to squared error loss ...
متن کاملThe optimal age-based replacement policy for systems subject to shocks
In this article, two different systems subject to shocks occurring based on a non-homogeneous Poisson process (NHPP) are analyzed. Type –I system is consisted of a single unit and type –II system is consisted of two parallel units in which both units operate identically and simultaneously. In type –I system occurrence of a shock causes system stopping and consequently will be received minimal r...
متن کامل