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He initially used the model to account for a pattern of behavior seen in animals that are being reinforced at fixed-intervals, for example every 2 minutes. [ 3 ] An animal that is well trained on such a fixed-interval schedule pauses after each reinforcement and then suddenly starts responding about two-thirds of the way through the new interval.
Models for recurrent events can be specified by considering the probability distribution for the number of recurrences in short intervals [, +), given the history of event occurrence before time . The intensity function describes the instantaneous probability of an event occurring at time t {\displaystyle t} , conditional on the process history ...
A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, [1] landslides, [2] or river discharge flows to occur. It is a statistical measurement typically based on historic data over an extended period, and is used usually for risk analysis.
In probability theory and statistics, the Poisson distribution (/ ˈ p w ɑː s ɒ n /) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1]
An absolutely continuous probability distribution is a probability distribution on the real numbers with uncountably many possible values, such as a whole interval in the real line, and where the probability of any event can be expressed as an integral. [19]
In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
The fixed degree of certainty pre-specified by the analyst, referred to as the confidence level or confidence coefficient of the constructed interval, is effectively the nominal coverage probability of the procedure for constructing confidence intervals.