# Modeling tail data using Generalized Pareto distribution

I just estimated a ARMA(1,1)+GARCH(1,1)+Threshold order(1) equation for time series of stock prices. Now I'm going to estimate the residuals' marginal distributions using the kernel density estimator in the interior of the distribution and the POT method in the tails using 10% of the data points for each tail. I calculated cdf for all tail points using estimated parameters $(\mu=-5.98,\sigma=36.342 ,\varepsilon=-7.04)$ but the function doesn't support all of data points in tails. $(\mu < x < \mu-\frac{\sigma}{\varepsilon})$ Am I supposed to fit GPD to all data not just tails? what are the other distributions appropriate for modeling tail data?