On Secondary Processes Generated by a Random Point Distribution of Poisson Type
نویسنده
چکیده
In the present paper we consider the mathematical model of secondary processes and give a general and rigorous method for solving special problems. We do not suppose that the basic “process” is a time-process but consider the problem more generally, i.e. we replace the time axis by an abstract space where the random points are distributed. The idea of our general method was suggested by a lecture of C. Ryll–Nardzewski, who gave an elegant solution of a telephone-problem.1 We shall return to this problem and its solution in § 3 (Example 3.) In § 1 we give a sufficient condition ensuring the Poisson character of a random point distribution. In § 2 the secondary process generated by a random point distribution of Poisson-type is considered and in § 3 some examples are given.
منابع مشابه
On Secondary Processes Generated by Random Point Distributions
In the paper [3] we have given a rigorous mathematical model and a general method for solving special problems in connection with secondary processes generated by a random point distribution of Poisson type. A random point distribution is a random selection of a finite or countably infinite number of points of an abstract set T where a σ-algebra ST is given. It is supposed that if ξ(A) denotes ...
متن کاملApplication of Gompertz-Poisson Distribution in LifetimeTheory
Gompertz-Poisson distribution is a three-parameter lifetime distribution with increasing, decreasing, increasing-decreasing and unimodal shape failure rate function and a composition of Gompertz and Poisson distributions cut at zero point that in this paper estimated the parameters of the distribution by maximum likelihood method and in order to confirm the calculated estimates, based on random...
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 کاملA Deterministic Displacement Theorem for Poisson Processes
We announce a deterministic analog of Bartlett’s displacement theorem. The result is that a Poisson property is stable with respect to deterministic Hamiltonian displacements. While the random point configurations move according to an n-body evolution, the mean measure P satisfies a nonlinear Vlasov type equation Ṗ + y · ∇xP − ∇y · E(P ) = 0. Combined with Bartlett’s theorem, the result general...
متن کاملApproximating Bayes Estimates by Means of the Tierney Kadane, Importance Sampling and Metropolis-Hastings within Gibbs Methods in the Poisson-Exponential Distribution: A Comparative Study
Here, we work on the problem of point estimation of the parameters of the Poisson-exponential distribution through the Bayesian and maximum likelihood methods based on complete samples. The point Bayes estimates under the symmetric squared error loss (SEL) function are approximated using three methods, namely the Tierney Kadane approximation method, the importance sampling method and the Metrop...
متن کامل