Records, Mixed Poisson Processes and Optimal Selection: An Intensity Approach
نویسنده
چکیده
We provide an analysis of the records process associated with a marked, general mixed Poisson process. In particular, we obtain a new representation of the intensity of the records process. This in turn allows a new probabilistic characterization of the exponential distribution as being the only mixing distribution for which the records process is exactly a Poisson process. As a corollary, we obtain a simple probabilistic proof of an important identity involving Stirling numbers. Our motivating example is an optimal selection problem in continuous time, which is solved for a variety of cases.
منابع مشابه
Factors Affecting Hospital Length of Stay Using Mixed Poisson Regression Models
Background and purpose: Modeling of Hospital Length of Stay (LOS) is of great importance in healthcare systems, but there is paucity of information on this issue in Iran. The aim of this study was to identify the optimal model among different mixed poisson distributions in modeling the LOS and effective factors. Materials and methods: In this cross-sectional study, we studied 1256 records, inc...
متن کاملSelection of Optimal Intensity Measure for Seismic Assessment of Steel Buckling Restrained Braced Frames under Near-Fault Ground Motions
Buckling restrained braces (BRBs) have a similar behavior under compression and tension loadings. Therefore, they can be applied as a favorable lateral load resisting system for structures. In the performance-based earthquake engineering (PBEE) framework, an intermediate variable called intensity measure (IM) links the seismic hazard analysis with the structural response analyses. An optimal IM...
متن کاملFractional Poisson Process
For almost two centuries, Poisson process with memoryless property of corresponding exponential distribution served as the simplest, and yet one of the most important stochastic models. On the other hand, there are many processes that exhibit long memory (e.g., network traffic and other complex systems). It would be useful if one could generalize the standard Poisson process to include these p...
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 کاملApplication of an integrated decision-making approach based on FDAHP and PROMETHEE for selection of optimal coal seam for mechanization; A case study of the Tazareh coal mine complex, Iran
Increasing the production rate and minimizing the related costs, while optimizing the safety measures, are nowadays’ most important tasks in the mining industry. To these ends, mechanization of mines could be applied, which can result in significant cost reductions and higher levels of profitability for underground mines. The potential of a coal mine mechanization depends on some important fact...
متن کامل