Degrees of freedom (statistics)In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom. In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself.
Poisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.
Characteristic function (probability theory)In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function. Thus it provides an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.
Moment-generating functionIn probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple results for the moment-generating functions of distributions defined by the weighted sums of random variables.
Convergence of random variablesIn probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied.
F-distributionIn probability 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 George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other F-tests. The F-distribution with d1 and d2 degrees of freedom is the distribution of where and are independent random variables with chi-square distributions with respective degrees of freedom and .
Pearson distributionThe Pearson distribution is a family of continuous probability distributions. It was first published by Karl Pearson in 1895 and subsequently extended by him in 1901 and 1916 in a series of articles on biostatistics. The Pearson system was originally devised in an effort to model visibly skewed observations. It was well known at the time how to adjust a theoretical model to fit the first two cumulants or moments of observed data: Any probability distribution can be extended straightforwardly to form a location-scale family.
CumulantIn probability theory and statistics, the cumulants κn of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa. The first cumulant is the mean, the second cumulant is the variance, and the third cumulant is the same as the third central moment. But fourth and higher-order cumulants are not equal to central moments.
Likelihood functionIn statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.
Chi distributionIn probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable and the origin. It is thus related to the chi-squared distribution by describing the distribution of the positive square roots of a variable obeying a chi-squared distribution.
