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In mathematics, a codomain or set of destination of a function is a set into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X → Y. The term range is sometimes ambiguously used to refer to either the codomain or the image of a function. A codomain is part of a function f if f is defined as a ...
correlation. so that. where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. ), which is called the variance and is more commonly denoted as ...
Increment theorem. In nonstandard analysis, a field of mathematics, the increment theorem states the following: Suppose a function y = f(x) is differentiable at x and that Δx is infinitesimal. Then. {\displaystyle \Delta y=f' (x)\,\Delta x+\varepsilon \,\Delta x} for some infinitesimal ε, where. If then we may write.
A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0- arity) predicates.
The Kendall tau distance between two series is the total number of discordant pairs. The Kendall tau rank correlation coefficient, which measures how closely related two series of numbers are, is proportional to the difference between the number of concordant pairs and the number of discordant pairs.
For a set of random variables X n and corresponding set of constants a n (both indexed by n, which need not be discrete), the notation = means that the set of values X n /a n converges to zero in probability as n approaches an appropriate limit. Equivalently, X n = o p (a n) can be written as X n /a n = o p (1), i.e.
A marginal value is. a value that holds true given particular constraints, the change in a value associated with a specific change in some independent variable, whether it be of that variable or of a dependent variable, or. [when underlying values are quantified] the ratio of the change of a dependent variable to that of the independent variable.
Second moment method. In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive. More generally, the "moment method" consists of bounding the probability that a random variable fluctuates far from its mean, by using its moments.