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In any given 100-year period, a 100-year event may occur once, twice, more, or not at all, and each outcome has a probability that can be computed as below. Also, the estimated return period below is a statistic: it is computed from a set of data (the observations), as distinct from the theoretical value in an idealized distribution. One does ...
For a single recurrent event process starting at =, let < < … denote the event times, where is the time of the th event. The associated counting process {(),} records the cumulative number of events generated by the process; specifically, () = = is the number of events occurring over the time interval [,].
where Pc is the cumulative probability and N is the number of data. It is seen that the standard deviation Sd reduces at an increasing number of observations N. The determination of the confidence interval of Pc makes use of Student's t-test (t). The value of t depends on the number of data and the confidence level of the estimate of the ...
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]
A frequency distribution shows a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc.
The terminal nodes indicate the number of subjects in the node, the number of subjects who have events, and the relative event rate compared to the root. In the node on the far left, the values 1/33 indicate that one of the 33 subjects in the node had an event, and that the relative event rate is 0.122.
A seasonal pattern exists when a time series is influenced by seasonal factors. Seasonality occurs over a fixed and known period (e.g., the quarter of the year, the month, or day of the week). [1], the irregular component (or "noise") at time t, which describes random, irregular influences. It represents the residuals or remainder of the time ...
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.