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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.
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount; Bhatia–Davis inequality, an upper bound on the variance of any bounded probability distribution; Bernstein inequalities (probability theory) Boole's inequality; Borell–TIS ...
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, [2] is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend ...
A random sample can be thought of as a set of objects that are chosen randomly. More formally, it is "a sequence of independent, identically distributed (IID) random data points." In other words, the terms random sample and IID are synonymous. In statistics, "random sample" is the typical terminology, but in probability, it is more common to ...
Dirichlet Random Measures, Method of Construction via Compound Poisson Random Variables, and Exchangeability Properties of the resulting Gamma Distribution SciencesPo : R package that contains functions for simulating parameters of the Dirichlet distribution.
The Fréchet distribution, also known as inverse Weibull distribution, [2] [3] is a special case of the generalized extreme value distribution.It has the cumulative distribution function
This breakthrough resulted in the understanding that the Bernoulli process is unique and universal; in a certain sense, it is the single most random process possible; nothing is 'more' random than the Bernoulli process (although one must be careful with this informal statement; certainly, systems that are mixing are, in a certain sense ...
Other generating functions of random variables include the moment-generating function, the characteristic function and the cumulant generating function. The probability generating function is also equivalent to the factorial moment generating function , which as E [ z X ] {\displaystyle \operatorname {E} \left[z^{X}\right]} can also be ...