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Covariant return types have been (partially) allowed in the Java language since the release of JDK5.0, [2] so the following example wouldn't compile on a previous release: // Classes used as return types: class A { } class B extends A { } // "Class B is narrower than class A" // Classes demonstrating method overriding: class C { A getFoo ...
An example is the compareTo method: a. compareTo (b) checks whether a comes before or after b in some ordering, but the way to compare, say, two rational numbers will be different from the way to compare two strings. Other common examples of binary methods include equality tests, arithmetic operations, and set operations like subset and union.
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
An N-point DFT is expressed as the multiplication =, where is the original input signal, is the N-by-N square DFT matrix, and is the DFT of the signal.. The transformation matrix can be defined as = (), =, …,, or equivalently:
The effect of these sources of randomness on the distribution of the inputs to internal layers during training is described as internal covariate shift. Although a clear-cut precise definition seems to be missing, the phenomenon observed in experiments is the change on means and variances of the inputs to internal layers during training.
The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in R p×p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator. [1]
An example is provided by the analysis of trend in sea-level by Woodworth (1987). [9] Here the dependent variable (and variable of most interest) was the annual mean sea level at a given location for which a series of yearly values were available. The primary independent variable was "time".
One possible solution to this anchor point placement problem is to remove the histogram binning grid completely. In the left figure below, a kernel (represented by the grey lines) is centred at each of the 50 data points above. The result of summing these kernels is given on the right figure, which is a kernel density estimate.