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Figure 1. A simple bimodal distribution, in this case a mixture of two normal distributions with the same variance but different means. The figure shows the probability density function (p.d.f.), which is an equally-weighted average of the bell-shaped p.d.f.s of the two normal distributions.
The mode of a sample is the element that occurs most often in the collection. For example, the mode of the sample [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] is 6. Given the list of data [1, 1, 2, 4, 4] its mode is not unique. A dataset, in such a case, is said to be bimodal, while a set with more than two modes may be described as multimodal.
The modal base here is the knowledge of the speaker, the modal force is necessity. By contrast, (5) could be paraphrased as 'Given his abilities, the strength of his teeth, etc., it is possible for John to open a beer bottle with his teeth'. Here, the modal base is defined by a subset of John's abilities, the modal force is possibility.
It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies , and inference apparatus with substitution and modus ponens , but extending the syntax with the modal operator necessarily {\displaystyle \Box } and its dual possibly {\displaystyle \Diamond } .
Modal windows are sometimes called heavy windows or modal dialogs because they often display a dialog box. User interfaces typically use modal windows to command user awareness and to display emergency states, though interaction designers argue they are ineffective for that use. [1] Modal windows are prone to mode errors. [1] [2] [3]
In application of modal logic to computer science, the so-called possible worlds can be understood as representing possible states and the accessibility relation can be understood as a program. Then w R v {\displaystyle wRv} iff running the program can transition the computer from state w {\displaystyle w} to state v {\displaystyle v} .
An estimation procedure that is often claimed to be part of Bayesian statistics is the maximum a posteriori (MAP) estimate of an unknown quantity, that equals the mode of the posterior density with respect to some reference measure, typically the Lebesgue measure.
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.If an arbitrarily large number of samples, each involving multiple observations (data points), were separately used to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample, then the sampling ...