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In decision theory, the weighted sum model (WSM), [1] [2] also called weighted linear combination (WLC) [3] or simple additive weighting (SAW), [4] is the best known and simplest multi-criteria decision analysis (MCDA) / multi-criteria decision making method for evaluating a number of alternatives in terms of a number of decision criteria.
In number theory, Ramanujan's sum, usually denoted c q (n), is a function of two positive integer variables q and n defined by the formula = (,) =,where (a, q) = 1 means that a only takes on values coprime to q.
If the integral of a function f is uniformly bounded over all intervals, and g is a non-negative monotonically decreasing function, then the integral of fg is a convergent improper integral. Notes [ edit ]
exists there are three possibilities: if L > 1 the series converges (this includes the case L = ∞) if L < 1 the series diverges; and if L = 1 the test is inconclusive. An alternative formulation of this test is as follows. Let { a n} be a series of real numbers. Then if b > 1 and K (a natural number) exist such that
^ = the maximized value of the likelihood function of the model , i.e. ^ = (^,), where {^} are the parameter values that maximize the likelihood function and is the observed data; n {\displaystyle n} = the number of data points in x {\displaystyle x} , the number of observations , or equivalently, the sample size;
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4]
When a preference function has been associated to each criterion by the decision maker, all comparisons between all pairs of actions can be done for all the criteria. A multicriteria preference degree is then computed to globally compare every couple of actions:
The sum ((,)) = + is a complete statistic for θ. To show this, it is sufficient to demonstrate that there is no non-zero function such that the expectation of ((,)) = (+) remains zero regardless of the value of θ.