{
  "id": "1812.06078",
  "version": "v1",
  "published": "2018-12-14T18:57:39.000Z",
  "updated": "2018-12-14T18:57:39.000Z",
  "title": "Stochastic comparisons between the extreme claim amounts from two heterogeneous portfolios in the case of transmuted-G model",
  "authors": [
    "Hossein Nadeb",
    "Hamzeh Torabi",
    "Ali Dolati"
  ],
  "categories": [
    "stat.AP"
  ],
  "abstract": "Let $X_{\\lambda_1}, \\ldots , X_{\\lambda_n}$ be independent non-negative random variables belong to the transmuted-G model and let $Y_i=I_{p_i} X_{\\lambda_i}$, $i=1,\\ldots,n$, where $I_{p_1}, \\ldots, I_{p_n}$ are independent Bernoulli random variables independent of $X_{\\lambda_i}$'s, with ${\\rm E}[I_{p_i}]=p_i$, $i=1,\\ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. In this paper we compare the smallest and the largest claim amounts of two sets of independent portfolios belonging to the transmuted-G model, in the sense of usual stochastic order, hazard rate order and dispersive order, when the variables in one set have the parameters $\\lambda_1,\\ldots,\\lambda_n$ and the variables in the other set have the parameters $\\lambda^{*}_1,\\ldots,\\lambda^{*}_n$. For illustration we apply the results to the transmuted-G exponential and the transmuted-G Weibull models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-14T18:57:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extreme claim amounts",
      "transmuted-g model",
      "stochastic comparisons",
      "heterogeneous portfolios",
      "non-negative random variables belong"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}