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In statistics, fractional factorial designs are experimental designs consisting of a carefully chosen subset (fraction) of the experimental runs of a full factorial design. [ 1] The subset is chosen so as to exploit the sparsity-of-effects principle to expose information about the most important features of the problem studied, while using a ...
The Pareto distribution is a continuous probability distribution. Zipf's law, also sometimes called the zeta distribution, is a discrete distribution, separating the values into a simple ranking. Both are a simple power law with a negative exponent, scaled so that their cumulative distributions equal 1.
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 :
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population ). A statistical model represents, often in considerably idealized form, the data-generating process. [ 1] When referring specifically to probabilities, the corresponding ...
Potentials. Scientists. v. t. e. Fermi–Dirac statistics is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul ...
The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 − p. 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 ...
Mode (statistics) In statistics, the mode is the value that appears most often in a set of data values. [ 1] If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e., x=argmaxxi P (X = xi) ). In other words, it is the value that is most likely to be sampled.
A contrast is defined as the sum of each group mean multiplied by a coefficient for each group (i.e., a signed number, c j ). [ 10] In equation form, , where L is the weighted sum of group means, the c j coefficients represent the assigned weights of the means (these must sum to 0 for orthogonal contrasts), and j represents the group means. [ 8]