{
  "id": "2310.06638",
  "version": "v1",
  "published": "2023-10-10T13:59:48.000Z",
  "updated": "2023-10-10T13:59:48.000Z",
  "title": "On the Superposition of Generalized Counting Processes",
  "authors": [
    "K. K. Kataria",
    "M. Dhillon"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study the merging of independent generalized counting processes (GCPs). First, we study the merging of finite number of independent GCPs and then extend it to the countably infinite case. It is observed that the merged process is a GCP with increased arrival rates. Some distributional properties of the merged process are obtained. It is shown that a packet of jumps arrives in the merged process according to Poisson process. An application to industrial fishing problem is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-10T13:59:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60G55"
    ],
    "keywords": [
      "merged process",
      "superposition",
      "increased arrival rates",
      "industrial fishing problem",
      "poisson process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}