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...

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

(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...

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...

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...

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