In distribution theory, the space Φ is characterized as a test-function space, where a test-function is thought of as a very well-behaved function (being continuous, n-times differentiable, having a bounded domain or at least dropping off exponentially beyond some finite range, etc).
A notable subset of well-behaved functions turns out to be that of absolutely continuous functions, i.e. those expressible as an integral of their own derivative.
In order to derive a well-behaved density function, the distribution from the Monte Carlo simulation has been fitted to a curve described by (11), where G is a gamma-distributed random variable with shape parameter r and scale parameter λ.
We will assume that all the consumers are rational in the sense that observed demand results from the maximisation of a well-behaved utility function subject to an individual budget constraint.
Varian (1982) showed that any data set (left{ mathbf {p}_{t},mathbf {q} _{t}^{h}right} _{tin tau }) that can be rationalised by a well-behaved utility function will also satisfy the Generalized Axiom of Revealed Preference (GARP).
The theorem thus implies that any data set (left{ mathbf {p}_{t},mathbf {q} _{t}^{h}right} _{tin tau }) that can be rationalised by a well-behaved utility function needs to satisfy the Afriat inequalities.
In both cases the cost functions are rather well-behaved functions away from the sensors.
We show that if the scaling factors are chosen randomly then the expected complexity of the union of the cubes is O(n log2 n), and it improves to O(n log n) if the scaling factors are chosen randomly from a "well-behaved" probability density function (pdf).
Deriving its roots from calculus, one is often concerned with minimizing a "well-behaved" (e.g. differentiable) function, where tools such as gradient descent, already introduced by Augustin Cauchy in 1847, can be applied.
He claims that this conception of rationality is implied by the fact that decision theorists are able to represent the rational actions of any agent possessing a well-behaved preference ordering as the maximization of a utility function.
Next, we review a class of parametric smooth functions, used to replace the complementarity conditions of the KKT conditions with a well-behaved, smoothed nonlinear equality constraint.
