theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and...

the noncentral F-distribution is a continuous probability distribution that is a noncentral generalization of the (ordinary) F-distribution. It describes...

-\infty }F(x)=0} and lim x → ∞ F ( x ) = 1 {\displaystyle \lim _{x\rightarrow \infty }F(x)=1} . In the case of a scalar continuous distribution, it gives...

theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable...

to the cumulative distribution functions of the beta distribution and of the F-distribution: F ( k ; n , p ) = F beta-distribution ( x = 1 − p ; α = n...

|}}\sim \operatorname {F} (2,2)} . (F-distribution) If X , Y ∼ U ( 0 , 1 ) {\displaystyle X,Y\sim {\textrm {U}}(0,1)} (uniform distribution) then log ⁡ ( X /...

calculates a statistic, represented by the random variable F, and checks if it follows an F-distribution. This check is valid if the null hypothesis is true...

the cumulative distribution function F {\displaystyle F} has the form F ( x ) = P ( X ≤ x ) = ∫ − ∞ x f ( t ) d t {\displaystyle F(x)=P(X\leq x)=\int...

statistics, the matrix F distribution (or matrix variate F distribution) is a matrix variate generalization of the F distribution which is defined on real-valued...

T-squared distribution (T2), proposed by Harold Hotelling, is a multivariate probability distribution that is tightly related to the F-distribution and is...

gamma distribution is a versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and...

distribution can be parametrized by a single scalar value α, called the concentration parameter. In terms of α, the density function has the form f (...

the point f ( x ) . {\displaystyle f(x).} Instead of acting on points, distribution theory reinterprets functions such as f {\displaystyle f} as acting...

distribution is the probability distribution of the test statistic when the null hypothesis is true. For example, in an F-test, the null distribution...

Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f (...

t-distribution Noncentral chi-squared distribution Noncentral chi-distribution Noncentral F-distribution Noncentral beta distribution In general, noncentrality parameters...

while the F-distribution originates from the ratio of two independent chi-squared distributed random variables. More general ratio distributions have been...

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

Score test It is also a component of the definition of the t-distribution and the F-distribution used in t-tests, analysis of variance, and regression analysis...

density function (pdf) of an exponential distribution is f ( x ; λ ) = { λ e − λ x x ≥ 0 , 0 x < 0. {\displaystyle f(x;\lambda )={\begin{cases}\lambda e^{-\lambda...

cumulative distribution function of a beta distribution can be expressed in terms of the cumulative distribution function of a binomial distribution with F beta...

probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a given number...

Many probability distributions that are important in theory or applications have been given specific names. The Bernoulli distribution, which takes value...

≤ x ≤ R, and f(x) = 0 if |x| > R. The parameter R is commonly referred to as the "radius" parameter of the distribution. The distribution arises as the...

that it is contained in the distribution's support. The probability density function of the continuous uniform distribution is f ( x ) = { 1 b − a for  a...

I) distribution, then the probability that X is greater than some number x, i.e., the survival function (also called tail function), is given by F ¯ (...

density function of the Rayleigh distribution is f ( x ; σ ) = x σ 2 e − x 2 / ( 2 σ 2 ) , x ≥ 0 , {\displaystyle f(x;\sigma )={\frac {x}{\sigma...

joint cumulative distribution function satisfies F X , Y ( x , y ) = F X ( x ) ⋅ F Y ( y ) {\displaystyle F_{X,Y}(x,y)=F_{X}(x)\cdot F_{Y}(y)} Two discrete...

statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization to random...

(1933) to describe a particle size distribution. The probability density function of a Weibull random variable is f ( x ; λ , k ) = { k λ ( x λ ) k − 1...