In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If...

probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability...

In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of...

In probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the...

divisibility (probability) Method of moments (probability theory) Stability (probability) Stein's lemma Characteristic function (probability theory) Lévy continuity...

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose...

called a bound variable.) The term "characteristic function" has an unrelated meaning in classic probability theory. For this reason, traditional probabilists...

The ROC curve is thus the sensitivity as a function of false positive rate. Given that the probability distributions for both true positive and false...

A;\\+\infty ,&x\not \in A.\end{cases}}} In probability theory, the characteristic function of any probability distribution on the real line is given by...

In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary...

In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment...

Kronecker delta function as a discrete analog of the Dirac delta function. In probability theory and statistics, the Dirac delta function is often used...

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically...

(GIS) Chapman–Kolmogorov equation Chapman–Robbins bound Characteristic function (probability theory) Chauvenet's criterion Chebyshev center Chebyshev's inequality...

with the same probability. Figure 2 and Figure 3 illustrate bimodal distributions. Other definitions of unimodality in distribution functions also exist...

In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution...

random variables with common characteristic function φ ( t ) {\displaystyle \varphi (t)} . The empirical characteristic function (ECF) defined as φ n ( t...

In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random...

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

Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses expected utility and probability to...

In probability and statistics, the quantile function is a function Q : [ 0 , 1 ] ↦ R {\displaystyle Q:[0,1]\mapsto \mathbb {R} } which maps some probability...

In probability theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence...

convolution/sum of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds...

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

transforms) Probability-generating functions Moment-generating functions Laplace transforms and Laplace–Stieltjes transforms Characteristic functions A proof...

In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes...

Number-theoretic transform Basis vectors Bispectrum Characteristic function (probability theory) Orthogonal functions Schwartz space Spectral density Spectral density...

n\in \mathbb {N} } , φ {\displaystyle \varphi } are the characteristic functions of some probability distributions μ n , μ {\displaystyle \mu _{n},\mu } respectively...

physicist Eugene Wigner, is the probability distribution defined on the domain [−R, R] whose probability density function f is a scaled semicircle, i.e...

likelihood function (particularly for one-parameter exponential families) Conjugate pairing of probability distributions, in the Fourier-analytic theory of characteristic...