Goodness-of-fit tests in Nevzorov's model (Q2740079)

This paper deals with the investigation of natural catastrophe claims in the presence of a trend. The authors assume that the yearly catastrophe claims are realizations of a sequence \(\{X_{i},\;i\geq 1\}\) of independent random variables with support \([0,+\infty)\) and continuous cumulative distribution functions \(\{F_{i},\;i\geq 1\}\). If \(F_{i}=F(x)^{\gamma^{i-1}},\) \(F(0)=0\) and \(F(x)\) is unspecified, the model is called semi-parametric. If \(F_{i}=F(x;A,\alpha)^{\gamma^{i-1}}\), and \(F(x)=\exp(-(Ax)^{-\alpha})\) is the Fréchet distribution, the model is called a three-parameter model. A goodness-of-fit test is obtained for these models.