Search results
Results from the WOW.Com Content Network
The binomial distribution is the PMF of k successes given n independent events each with a probability p of success. Mathematically, when α = k + 1 and β = n − k + 1, the beta distribution and the binomial distribution are related by [clarification needed] a factor of n + 1:
The Rademacher distribution, which takes value 1 with probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same probability of success.
Beta distribution, for a single probability (real number between 0 and 1); conjugate to the Bernoulli distribution and binomial distribution Gamma distribution , for a non-negative scaling parameter; conjugate to the rate parameter of a Poisson distribution or exponential distribution , the precision (inverse variance ) of a normal distribution ...
Some distributions have been specially named as compounds: beta-binomial distribution, Beta negative binomial distribution, gamma-normal distribution. Examples: If X is a Binomial( n , p ) random variable, and parameter p is a random variable with beta( α , β ) distribution, then X is distributed as a Beta-Binomial( α , β , n ).
In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified/constant/fixed number of successes occur. [2]
The beta-binomial distribution is the binomial distribution in which the probability of success at each of n trials is not fixed but randomly drawn from a beta distribution. It is frequently used in Bayesian statistics, empirical Bayes methods and classical statistics to capture overdispersion in binomial type distributed data.
Compounding a binomial distribution with probability of success distributed according to a beta distribution yields a beta-binomial distribution. It possesses three parameters, a parameter n {\displaystyle n} (number of samples) from the binomial distribution and shape parameters α {\displaystyle \alpha } and β {\displaystyle \beta } from the ...
In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. The concept is named after Siméon Denis Poisson.