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The Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables.
The number of claims N is a random variable, which is said to have a "claim number distribution", and which can take values 0, 1, 2, .... etc..For the "Panjer recursion", the probability distribution of N has to be a member of the Panjer class, otherwise known as the (a,b,0) class of distributions.
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
Unlike a probability, a probability density function can take on values greater than one; for example, the continuous uniform distribution on the interval [0, 1/2] has probability density f(x) = 2 for 0 ≤ x ≤ 1/2 and f(x) = 0 elsewhere.
Furthermore, it was shown by Fackler [2] that there is a universal formula for all three distributions, called the (united) Panjer distribution. The more usual parameters of these distributions are determined by both a and b. The properties of these distributions in relation to the present class of distributions are summarised in the following ...
Suppose G is a p × n matrix, each column of which is independently drawn from a p-variate normal distribution with zero mean: = (, …,) (,). Then the Wishart distribution is the probability distribution of the p × p random matrix [4]
A diagram of an alias table that represents the probability distribution〈0.25, 0.3, 0.1, 0.2, 0.15〉 In computing, the alias method is a family of efficient algorithms for sampling from a discrete probability distribution, published in 1974 by Alastair J. Walker.
These five trees are each assigned probability 1/5 by the uniform distribution (top). The distribution generated by random insertion orderings (bottom) assigns the center tree probability 1/3, because two of the six possible insertion orderings generate the same tree; the other four trees have probability 1/6.