Limit Distributions Of Extremes From T And Skew-t Distributions

This paper mainly includes two parts which considers the asymptotics of extremes from Student-t and skew-t distributions respectively.The first part of the thesis firstly derive the tail representation of T-distribution, which shows that the T-distribution belongs to the domain of attraction of Φv(x). The norming constants are also obtained. Furthermore. we establish the asymptotic expansion of extreme-value distribution from t-distribution and also derive its associated pointwise convergence rate. The pointwise convergence rate of distribution of maximum from finite mixture t-distributions also is derived.In the second part, we further considers some properties of skew-t distribution which include the tail behavior, the Mills-type inequality and the Mills-type ratio, and the limit distributions of maximum and minimum from shew-t distribution are derived.