Characteristic function (probability theory)Fourier transform of the probability density functionThe characteristic function of a uniform U(–1,1) random variable. This function is real-valued because it corresponds to a random variable that is symmetric around the origin; however characteristic functions may generally be complex-valued.In probability theory and statistics, the characteristic function of any real-valuedrandom variable completely defines its probability distribution.
Probability density functionIn probability theory, a probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given point in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a "relative probability" that the value of the random variable would be equal to that point. Probability density is the probability per unit length, in other words.
Moment (mathematics)Moments of a function in mathematics are certain quantitative measures related to the shape of the function's graph. For example, if the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia.
Generating functionFormal power seriesIn mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series. There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series.Two-sided Laplace transformIn mathematics, the two-sided Laplace transform or bilateral Laplace transform is an integral transform equivalent to probability's moment-generating function. Two-sided Laplace transforms are closely related to the Fourier transform, the Mellin transform, the Z-transform and the ordinary or one-sided Laplace transform.
Probability distributionMathematical function for the probability a given outcome occurs in an experimentIn probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more precisely, to events, which are sets of possible outcomes of a probabilistic experiment. Informally, a probability distribution tells us how likely different results are.Cumulative distribution functionProbability that random variable X is less than or equal to xCumulative distribution function for the exponential distributionCumulative distribution function for the normal distributionIn probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variableX{\displaystyle X}, or just distribution function of X{\displaystyle X}, evaluated at x{\displaystyle x}, is the probability that X{\displaystyle X} will take a value less than or equal to x{\displaystyle x}.
Expected valueAverage value of a random variableIn probability theory, the expected value (also called expectation, mean, or first moment) is a generalization of the weighted average. Provided that it is finite, the expected value can be interpreted as the long-run average of results from independent repetitions of the same random experiment, as formalized by the law of large numbers.Random variableVariable representing a random phenomenonA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.Multivariate random variableIn probability and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped together because they are all part of a single mathematical system — often they represent different properties of an individual statistical unit.
Probability theoryProbability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.
StatisticsStatistics (from German: Statistik, orig. "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.*As an Amazon Associate I earn from qualifying purchases.