{
  "id": "2209.01516",
  "version": "v1",
  "published": "2022-09-04T02:01:44.000Z",
  "updated": "2022-09-04T02:01:44.000Z",
  "title": "Generalized Bernoulli process and fractional binomial distribution II",
  "authors": [
    "Jeonghwa Lee"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Bernoulli process is a sequence of independent binary random variables, and binomial distribution concerns probabilities regarding its cumulative sum. Recently, a generalized Bernoulli process(GBP-I) was developed in which binary random variables are correlated with its covariance function obeying power law. The resulting sum of a finite sequence in GBP-I, called fractional binomial random variable, has variance asymptotically proportional to a fractional power of the length of the sequence. In this paper, we propose a different generalized Bernoulli process(GBP-II). It turns out that there is an interesting connection between GBP-II and fractional Poisson process. Similarities and differences between GBP-I, GBP-II, and fractional Poisson process are examined theoretically and empirically with simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-04T02:01:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized bernoulli process",
      "fractional binomial distribution",
      "function obeying power law",
      "fractional poisson process",
      "binary random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}