Mameli, Valentina (2012) *Two generalizations of the skew-normal distribution and two variants of McCarthy's theorem.* [Doctoral Thesis]

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## Abstract

The thesis is structured into two main parts. The first and major part is concerned with the skew-normal distribution, introduced by Azzalini (1985) [6], while the second one is connected with the scoring rules. In part one the problem of finding confidence intervals for the skewness parameter of the skew-normal distribution is addressed. Two new five-parameter continuous distributions which generalize the skew-normal distribution as well as some other well-known distributions are proposed and studied. Some mathematical properties of both distributions are derived. Part two is focused on the extension of the theorem of characterization of scoring rules, due to McCarthy (1956) ([16] of part 2), in two directions: for countable infinite sample spaces, but with bounded score and for finite sample spaces, but with unbounded score.

Item Type: | Doctoral Thesis |
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Date: | 29 March 2012 |

Tutor: | Musio, Monica |

PhD classes: | Ciclo 23 > Matematica e calcolo scientifico |

Coordinator: | D'Ambra Giuseppina |

Institution: | Universita' degli Studi di Cagliari |

Divisions: | Dipartimenti (fino a dicembre 2011) > Dipartimento di Matematica e informatica |

Subjects: | Area 01 - Scienze matematiche e informatiche > MAT/06 Probabilità e statistica matematica |

Uncontrolled Keywords: | Distribuzione skew-normal, distribuzione beta, distribuzione Kumaraswamy, teorema di McCarthy, skew-normal distribution, beta distribution, kumaraswamy distribution, McCarthy's theorem |

ID Code: | 756 |

Deposited On: | 30 Mar 2012 12:39 |

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