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In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables.
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The Panjer recursion makes use of this iterative relationship to specify a recursive way of constructing the probability distribution of S. In the following W N ( x ) {\displaystyle W_{N}(x)\,} denotes the probability generating function of N : for this see the table in (a,b,0) class of distributions .
In probability theory, an event is a set 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]
Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...
Probability function or probability measure: describes the probability () that the event , occurs. [ 11 ] Cumulative distribution function : function evaluating the probability that X {\displaystyle X} will take a value less than or equal to x {\displaystyle x} for a random variable (only for real-valued random variables).
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The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...