. Since some formulas below were derived for the left-tail case and some for the right-tail case, the following reconciliations can be useful: and . Normal distribution If the payoff of a portfolio follows normal (Gaussian) distribution with the p.d.f. then the left-tail TVaR is equal to , where is the standard normal p.d.f., is the standard normal c.d.f., so is the standard normal quantile. If the loss of a portfolio follows normal distribution, the right-tail TVaR is equal to . Generalized Student's t-distribution If the payoff of a portfolio follows generalized Student's t-distribution with the p.d.f. then the left-tail TVaR is equal to , where is the standard t-distribution p.d.f., is the standard t-distribution c.d.f., so is the standard t-distribution quantile. If the loss of a portfolio follows generalized Student's t-distribution, the right-tail TVaR is equal to . Laplace distribution If the payoff of a portfolio follows Laplace distribution with the p.d.f. and the c.d.f. then the left-tail TVaR is equal to for . If the loss of a portfolio follows Laplace distribution, the right-tail TVaR is equal to . Logistic distribution If the payoff of a portfolio follows logistic distribution with the p.d.f. and the c.d.f. then the left-tail TVaR is equal to . If the loss of a portfolio follows logistic distribution, the right-tail TVaR is equal to . Exponential distribution If the loss of a portfolio follows exponential distribution with the p.d.f. and the c.d.f. then the right-tail TVaR is equal to . Pareto distribution If the loss of a portfolio follows Pareto distribution with the p.d.f. and the c.d.f. then the right-tail TVaR is equal to . Generalized Pareto distribution (GPD) If the loss of a portfolio follows GPD with the p.d.f. and the c.d.f. then the right-tail TVaR is equal to and the VaR is equal to . Weibull distribution If the loss of a portfolio follows Weibull distribution with the p.d.f. and the c.d.f. then the right-tail TVaR is equal to , where is the upper incomplete gamma function. Generalized extreme value distribution (GEV) If the payoff of a portfolio follows GEV with the p.d.f. and the c.d.f. then the left-tail TVaR is equal to and the VaR is equal to , where is the upper incomplete gamma function, is the logarithmic integral function. If the loss of a portfolio follows GEV, then the right-tail TVaR is equal to , where is the