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The kth percentile P_k is that value of x, say x_k, which corresponds to a cumulative frequency of Nk/100, where N is the sample size.

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

The function f(x,y)=(1-x)^2+100(y-x^2)^2 that is often used as a test problem for optimization algorithms (where a variation with 100 replaced by 105 is sometimes used; ...

For a given bounded function f(x) over a partition of a given interval, the upper sum is the sum of box areas M^*Deltax_k using the supremum M of the function f(x) in each ...

Using disk point picking, x = sqrt(r)costheta (1) y = sqrt(r)sintheta (2) for r in [0,1], theta in [0,2pi), choose two points at random in a unit disk and find the ...

A sufficient condition on the Lindeberg-Feller central limit theorem. Given random variates X_1, X_2, ..., let <X_i>=0, the variance sigma_i^2 of X_i be finite, and variance ...

There are infinitely many primes m which divide some value of the partition function P.

The mode of a set of observations is the most commonly occurring value. For example, for a data set (3, 7, 3, 9, 9, 3, 5, 1, 8, 5) (left histogram), the unique mode is 3. ...

The conjecture that all integers >1 occur as a value of the totient valence function (i.e., all integers >1 occur as multiplicities). The conjecture was proved by Ford ...

The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 2000, p. 6). The survival function is therefore ...