Rechterstaart

Rechterstaart is a term used in probability theory and statistics to denote the portion of a distribution that lies on the high-value end. It is defined relative to a threshold or central location, and contrasts with the linkerstaart (the lower-value end).

Given a random variable X with cumulative distribution function F, the right-tail probability above x is P(X > x) = 1 − F(x). For a probability density f on (−∞, ∞), the right tail corresponds to the integral from x to ∞ of f(t) dt. In discrete distributions, the right tail comprises outcomes with values above the threshold.

Key concepts associated with the rechterstaart include tail quantiles, survival function, and tail index. In heavy-tailed distributions, the right tail decays slowly, and tail behavior is often summarized by asymptotics such as P(X > x) ~ L(x) x^−α or by models like the Pareto or lognormal. Tail estimation in data often uses empirical survival probabilities, Hill estimators for the tail index, or threshold-based methods in extreme value theory. The choice of threshold and sample size critically affects accuracy.

Applications of rechterstaart analysis appear in risk assessment, finance, meteorology, and engineering, where understanding the probability of extreme high outcomes is important. In finance, the right tail can relate to upside potential or, in some contexts, to tail risks when focusing on extreme gains or losses beyond a threshold. See also: linkerstaart, upper tail, tail distribution, survival function, extreme value theory.