(probability theory) Clipping of probability density function. [(probability theory) Any function whose integral over a set gives the probability that a random variable has a value in that set]

(mathematics) With regard to differentiation

(mathematics, physics) A function of seven variables of the form f(x,y,z,t;v_x,v_y,v_z) that gives the number of particles per unit volume in single-particle phase space.

(mathematics) An infinitesimal interval of a quantity, a differential.

(mathematics) An arbitrarily small quantity.

(mathematics) Pertaining to mathematical analysis using explicit error bound estimation and the epsilon-delta definition of a limit, especially as opposed to using infinitesimals.

(statistics, engineering) Of or relating to a process in which every sequence or sample of sufficient size is equally representative of the whole.

(mathematical analysis) The supremum (least upper bound) of a function which holds almost everywhere. In symbols, ess sup f= inf M:𝜇(x:f(x)>M)=0

(statistics) Any of a class of continuous probability distributions used to model the time between events that occur independently at a constant average rate.

(mathematics) Any solution to a variety of equations in the calculus of variations

(mathematics) A continued fraction which terminates after a certain number of steps.

(mathematics) Any of a finite number of discrete elements of a system, interconnected at discrete nodes, used to model a physical system

(mathematics) A value which is unchanged by a function or other mapping. Formally: a value x for which f(x) = x.ᵂ

(probability theory, statistics) Any of a family of two-parameter continuous probability distributions, of which the common exponential distribution and chi-square distribution are special cases.

(mathematics) the Gaussian function.

(mathematics, measure theory) A property that is true almost everywhere in a given set (i.e., the set of points at which the property is not true is either of measure zero or a subset of a set of measure zero).

(statistics) A generalization of the canonical ensemble to infinite systems, giving the probability of a given system being in a given state (or, equivalently, of a given random variable having a given value).

(mathematics) A behaviour of the Fourier series approximation at a jump discontinuity of a piecewise continuously differentiable periodic function, such that partial sums exhibit an oscillation peak adjacent the discontinuity that may overshoot the function maximum (or minimum) itself and does not disappear as more terms are calculated, but rather approaches a finite limit.

(mathematics) An element in a function's domain where the function assumes its lowest value.

(probability, statistics) A continuous probability distribution, often used to describe adult lifespans.

(probability theory, statistics) A model of the distribution of the maximum (or the minimum) of a number of samples of various distributions.

(statistics, countable) A parameterized set of probability distributions.

(probability theory, statistics) A random variable whose probability distribution is a hypergeometric distribution.

(mathematics) An imaginary quantity.

(algebra) In an equation, any variable whose value is not dependent on any other in the equation.

(mathematics) (of a subset) the greatest element of the containing set that is smaller than or equal to all elements of the subset. The infimum may or may not be a member of the subset.

(mathematics) A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).

(mathematics) The limit of the change in position per unit time as the unit of time approaches zero; expressed mathematically as lim _(t→0)(𝛥x)/(𝛥t)

(mathematics, historical or obsolete) The fluent of a given fluxion in Newtonian calculus.

(mathematics, attributive) describing a particular recurrence relation on a function space

(mathematics) A section that will not vary through changing state.

(mathematics) A system of iterated functions used to construct fractals

The probability distribution of a random variable whose sample space is the Cartesian product of the sample spaces of its (at least two) component random variables.

(mathematical analysis) A generalization of the hyperfactorial function in mathematics to real and complex numbers.

(mathematical analysis) The lower limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the "first subsequence." Then remove the first term of the first subsequence in order to obtain the "second subsequence." Repeat the removal of first terms in order to obtain a "third subsequence," "fourth subsequence," etc. Find the infimum of each of these subsequences, then find the supremum of all of these infimums. This supremum is the lower limit.

(mathematical analysis) A subset of a given measurable space which is a member of the σ-algebra of that space.

(statistical mechanics) A probability measure on the space of all thermodynamic states of a system

(mathematics, obsolete) An old kind of calculus in which lines were considered as made up of an infinite number of points; surfaces, as made up of an infinite number of lines; and volumes, as made up of an infinite number of surfaces.

(mathematics) The mex of a subset of a well-ordered set is the smallest value from the whole set that does not belong to the subset.

(mathematics) Any member of two families of probability distributions defined with the Mittag-Leffler function.

(mathematics) A function derived from the probability distribution of a random variable.

(mathematics, of a function) always increasing or remaining constant, and never decreasing; contrast this with strictly increasing

(mathematics) A function to be maximized or minimized in optimization theory.

(statistics) The curve of a cumulative distribution function.

(mathematics) generalization of the definition of a partition function in statistical mechanics

Initialism of probability density function. [(probability theory) Any function whose integral over a set gives the probability that a random variable has a value in that set]

(mathematics) Any function that applies constraints to a maximum or minimum problem

(mathematics) Any function whose value repeats after the regular addition of a period to its independent variable; i.e., a function ƒ such that, for some positive constant p, ƒ(x + p) = ƒ(x) for all x.

(mathematics, physics) A probability measure Φ on the σ-algebra of Borel sets of the unit square [0,1]² such that Φ has uniform marginals (that is, Φ ([α, β] × [0,1]) = Φ ([0,1] × [α, β]) = β − α for every 0 ≤ α ≤ β ≤ 1).

(mathematics) The Poisson distribution.

(probability theory) probability density function

(mathematics) A function that gives the relative probability that a discrete random variable is exactly equal to some value.

(mathematics) A mathematical measure on a probability space that can take on values between 0 and 1, with 0 corresponding to the empty set and 1 to the entire space.

(mathematics) A measurable space having a unit measure

The probit function, the inverse of the cumulative distribution function.

(mathematics, of a function) Such that an increment of a variable leads to a multiplication by some function.

(mathematics)

(mathematics) The set of values (points) which a function can obtain.

(mathematics) Describing a family of codes whose higher rate codes have codewords that are prefixes of those of the lower rate codes.

(mathematics, stochastic processes) A square matrix whose rows consist of nonnegative real numbers, with each row summing to 1. Used to describe the transitions of a Markov chain; its element in the i'th row and j'th column describes the probability of moving from state i to state j in one time step.

(mathematics) (of a function) That it is continuous almost everywhere, except at certain points at which it is either upper semi-continuous or lower semi-continuous.

(mathematical analysis) (Of a measure space) in which every nonzero measurable set has a subset with finite nonzero measure

(algebra) An algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse.

(mathematics) Half the number of zero crossings in the time base of a Walsh function.

(mathematical analysis) Alternative form of σ-additivity [(mathematical analysis) countable additivity]

(mathematics) Describing a set of numbers, none of which is as great as the sum of all the rest

(mathematics)

(mathematics, of a function) Having a Lebesgue integral.

(mathematics) A particular form or development

(mathematics) Describing a theory that is k-stable for all sufficiently large cardinals k.

(mathematics) Having the property that any nonempty subset has a finitely additive left-invariant measure that maps that subset to 1.

(mathematics) A symmetric probability distribution wherein every outcome is equally likely to occur at any point in the distribution.

(mathematical statistics) The operation of adding an extra parameter to the exponent of a density or distribution function.

(mathematics) Having intuitive, easy to handle properties, especially: having a finite derivative of all orders at all points, and having no discontinuities.

(statistics) A generalisation of the chi-square distribution to an arbitrary (integer) number of dimensions, or of the gamma distribution to a non-integer number of degrees of freedom.

(mathematical analysis) A set, in a measurable space, that is expressible as a countable union of sets of finite measure.