On the use of the generalized poisson distribution in actuarial statistics

• Emilio Gómez Déniz ^[1] ; Francisco José Vázquez Polo ^[1] ; José María Pérez Sánchez ^[1] ; Enrique Calderín Ojeda ^[1]
  1. [1] Universidad de Las Palmas de Gran Canaria

     Universidad de Las Palmas de Gran Canaria

     Gran Canaria, España

     
• Localización: Contributions to risk analysis: risk 2018 / coord. por José María Sarabia Alegría, Faustino Prieto Mendoza, Montserrat Guillén Estany, 2018, ISBN 978-84-9844-683-8, págs. 187-196
• Idioma: español
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this work a particular case of the generalized Poisson distribution is considered. This particular case derives in a one parameter distribution, more specifically the Borel- Tanner distribution, which result simple and appropriate in insurance setting. The distribution is unimodal with a zero vertex and overdispersed (mean larger than the variance). We revise some of its properties which have not been showed in the statistical literature and the estimation of the parameter, including the case when regression is considered. Expected frequencies were calculated for some examples, providing a very satisfactory fit. Finally, a conjugate distribution is considered and the resulting mixture distribution is studied.