Search results
Results from the WOW.Com Content Network
The concept of infinite divisibility of probability distributions was introduced in 1929 by Bruno de Finetti. This type of decomposition of a distribution is used in probability and statistics to find families of probability distributions that might be natural choices for certain models or applications.
The Poisson distribution, the stuttering Poisson distribution, [citation needed] the negative binomial distribution, and the Gamma distribution are examples of infinitely divisible distributions — as are the normal distribution, Cauchy distribution and all other members of the stable distribution family. The skew-normal distribution is an ...
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Help; Learn to edit; Community portal; Recent changes; Upload file
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
The generalized normal distribution; The geometric stable distribution; The Gumbel distribution; The Holtsmark distribution, an example of a distribution that has a finite expected value but infinite variance. The hyperbolic distribution; The hyperbolic secant distribution; The Johnson SU distribution; The Landau distribution; The Laplace ...
The normal distribution is the basis for the charts and requires the following assumptions: The quality characteristic to be monitored is adequately modeled by a normally distributed random variable; The parameters μ and σ for the random variable are the same for each unit and each unit is independent of its predecessors or successors
Since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal (known as a z-score) and then use the standard normal table to find probabilities. [2]
The distribution of a Lévy process has the property of infinite divisibility: given any integer n, the law of a Lévy process at time t can be represented as the law of the sum of n independent random variables, which are precisely the increments of the Lévy process over time intervals of length t/n, which are independent and identically ...