Estimation and approximation of tempered stable distribution

Tempered stable random variables have a LePage like series representation, which was first introduced by Rosinski. In this dissertation, we study the accuracy of the Rosinski representation as determined by the convergence rates of the series. We also study estimators of parameters of certain tempered stable distributions and construct their confidence intervals. Finally, we present several simulation results for the Gamma-tempered random variable.;Keywords. Tempered stable distribution, convergence rate, parameter estimation.