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In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]
Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature.
For example, the velocity of money is defined as nominal GDP / nominal money supply; it has units of (dollars / year) / dollars = 1/year. In discrete time , the change in a stock variable from one point in time to another point in time one time unit later (the first difference of the stock) is equal to the corresponding flow variable per unit ...
The full Laplace transform is the curve of all present values, plotted as a function of interest rate. For discrete time, where payments are separated by large time periods, the transform reduces to a sum, but when payments are ongoing on an almost continual basis, the mathematics of continuous functions can be used as an approximation.)
One may speak of infinite divisibility, or the lack thereof, of matter, space, time, money, ... data on securities prices are reported at discrete times. For example ...
It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it were a continuous distribution. The Kent distribution on the two-dimensional sphere.
A Divisia index is a theoretical construct to create index number series for continuous-time data on prices and quantities of goods exchanged. The name comes from François Divisia who first proposed and formally analyzed the indexes in 1926, and discussed them in related 1925 and 1928 works.
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal.