In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary...

Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also...

distributed Bernoulli variables. The Poisson distributions are infinitely divisible probability distributions.: 233 : 164  The directed Kullback–Leibler divergence...

1061/(ASCE)0733-9429(1990)116:7(946). Thorin, Olof (1977). "On the infinite divisibility of the lognormal distribution". Scandinavian Actuarial Journal....

distribution, we write X ~ Exp(λ). The exponential distribution exhibits infinite divisibility. The cumulative distribution function is given by F ( x ; λ ) =...

Infinite divisibility (probability) Method of moments (probability theory) Stability (probability) Stein's lemma Characteristic function (probability...

probability theory and statistics, Student's t distribution (or simply the t distribution) t ν {\displaystyle t_{\nu }} is a continuous probability distribution...

negative binomial distribution is infinitely divisible. The following recurrence relations hold: For the probability mass function { ( k + 1 ) Pr ( X =...

In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution...

{\mu }{n}}+X_{i}-Y_{i}\right)\sim {\textrm {Laplace}}(\mu ,b)} (infinite divisibility) If X has a Laplace distribution, then Y = eX has a log-Laplace...

In probability theory and statistics, the χ 2 {\displaystyle \chi ^{2}} -distribution with k {\displaystyle k} degrees of freedom is the distribution...

identically distributed by assumptions 2 and 3. Conversely, for each infinitely divisible probability distribution F {\displaystyle F} , there is a Lévy process...

parameters, see Mathai or Moschopoulos. The gamma distribution exhibits infinite divisibility. If X ∼ G a m m a ( α , θ ) , {\displaystyle X\sim \mathrm {Gamma}...

Every infinitely divisible probability distribution is a limit of compound Poisson distributions. And compound Poisson distributions is infinitely divisible...

In probability theory, a degenerate distribution on a measure space ( E , A , μ ) {\displaystyle (E,{\mathcal {A}},\mu )} is a probability distribution...

both divisible by this prime is 1/p2, and the probability that at least one of them is not is 1 − 1/p2. For distinct primes, these divisibility events...

Inferential statistics – redirects to Statistical inference Infinite divisibility (probability) Infinite monkey theorem Influence diagram Info-gap decision theory...

x 0 {\displaystyle x_{0}} . The Cauchy distribution is an infinitely divisible probability distribution. It is also a strictly stable distribution. Like...

chi-squared distributions. Cramér's theorem Cochran's theorem Infinite divisibility (probability) Khinchin's theorem on the factorization of distributions...

In probability theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions...

The Skellam distribution is the discrete probability distribution of the difference N 1 − N 2 {\displaystyle N_{1}-N_{2}} of two statistically independent...

that such reasoning can be extended to infinitely many divisibility events, one is led to guess that the probability that two numbers are coprime is given...

The Erlang distribution is a two-parameter family of continuous probability distributions with support x ∈ [ 0 , ∞ ) {\displaystyle x\in [0,\infty )}...

Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined as the normal variance-mean mixture where...

famous treatment. In 1929, de Finetti introduced the concept of infinitely divisible probability distributions. He also introduced de Finetti diagrams for graphing...

Algebra of random variables Relationships among probability distributions Infinite divisibility (probability) Bernoulli distribution Binomial distribution...

{\textstyle {\frac {\sigma ^{2}}{n}}} . This property is called infinite divisibility. Conversely, if X 1 {\textstyle X_{1}} and X 2 {\textstyle X_{2}}...

Many different uses in mathematics; see Asterisk § Mathematics. | 1.  Divisibility: if m and n are two integers, m ∣ n {\displaystyle m\mid n} means that...

distribution. The Kaniadakis κ-Erlang distribution has the following probability density function: f κ ( x ) = 1 ( n − 1 ) ! ∏ m = 0 n [ 1 + ( 2 m − n...

taken instead of the maximum is available by a simple extension. Infinite divisibility Indecomposable distribution Lukacs, E. (1970) Section 5.7 Feller...