tidsdistributions

Tidsdistributions are probability distributions that model the timing of events or the lengths of time intervals. They quantify uncertainty about quantities such as interarrival times in a renewal process, lifetimes of components, incubation or reaction times, and waiting times in queues. In practice, a tidsdistribution is described by a nonnegative random variable T with distribution function F(t) = P(T ≤ t) and, when applicable, a density f(t).

Common families include the exponential and gamma/Erlang distributions for waiting and interarrival times, the Weibull distribution for failure and lifetime analysis, and the log-normal or heavy-tailed distributions for multiplicative or extreme-time processes. More flexible approaches use mixtures or nonparametric estimates. Time-to-event data may be right-censored, left-truncated, or interval-censored, which affects how the distributions are estimated and interpreted.

Key quantities associated with tidsdistributions are the cumulative distribution function F(t), the probability density function f(t), the survival function S(t) = 1 − F(t), and the hazard function h(t) = f(t)/S(t). Moments such as the mean and variance describe central tendency and dispersion, while the tail behavior informs risk or reliability assessments. Parameter estimation typically uses maximum likelihood or method-of-moments; nonparametric survival analysis, such as the Kaplan–Meier estimator, handles censored data.

Applications span queuing theory, reliability engineering and maintenance planning, epidemiology and pharmacokinetics, finance (time to default or time between events), and cognitive or neuroscience research (response times). The choice of distribution depends on data characteristics, including skewness, tail heaviness, and whether the process is stationary or time-inhomogeneous.