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(Note that effective interest rates can only be defined as adimensional quantities.) In financial analysis, bond duration can be defined as (dV/dr)/V, where V is the value of a bond (or portfolio), r is the continuously compounded interest rate and dV/dr is a derivative. From the previous point, the dimension of r is 1/time.
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. [1] [2] In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. [3]
In contrast, probabilistic measurement models known as the Rasch model and Item response theory models are generally employed in the social sciences. Psychometrics is the field of study concerned with the theory and technique for measuring social and psychological attributes and phenomena. This field is central to much quantitative research ...
Information theory often concerns itself with measures of information of the distributions associated with random variables. One of the most important measures is called entropy, which forms the building block of many other measures. Entropy allows quantification of measure of information in a single random variable. [27]
developing ways to measure the hypothetical constructs proposed by the theory; empirically testing the hypothesized relations [1] Many psychologists noted that an important role of construct validation in psychometrics was that it placed more emphasis on theory as opposed to validation. This emphasis was designed to address a core requirement ...
When the underlying measure on (, ()) is finite, the distribution function in Definition 3 differs slightly from the standard definition of the distribution function (in the sense of probability theory) as given by Definition 2 in that for the former, = while for the latter, () = = ().
An important special case is that of inertial reference frames, a stationary or uniformly moving frame. For n dimensions, n + 1 reference points are sufficient to fully define a reference frame. Using rectangular Cartesian coordinates , a reference frame may be defined with a reference point at the origin and a reference point at one unit ...
This measure space is not σ-finite, because every set with finite measure contains only finitely many points, and it would take uncountably many such sets to cover the entire real line. The σ-finite measure spaces have some very convenient properties; σ-finiteness can be compared in this respect to the Lindelöf property of topological spaces.