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This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
dc: "Desktop Calculator" arbitrary-precision RPN calculator that comes standard on most Unix-like systems. KCalc, Linux based scientific calculator; Maxima: a computer algebra system which bignum integers are directly inherited from its implementation language Common Lisp. In addition, it supports arbitrary-precision floating-point numbers ...
We sample s-dimensional random vector U and mix it with {x 1, ..., x N}. In detail, for each x j, create = + and use the sequence () instead of (). If we have R replications for Monte Carlo, sample s-dimensional random vector U for each replication. Randomization allows to give an estimate of the variance while still using quasi-random sequences.
In estimating the population variance from a sample when the population mean is unknown, the uncorrected sample variance is the mean of the squares of deviations of sample values from the sample mean (i.e., using a multiplicative factor 1/n). In this case, the sample variance is a biased estimator of the population variance. Multiplying the ...
A i is the number of data type A at sample site i, B i is the number of data type B at sample site i, K is the number of sites sampled and || is the absolute value. This index is probably better known as the index of dissimilarity (D). [44] It is closely related to the Gini index. This index is biased as its expectation under a uniform ...
This calculator program has accepted input in infix notation, and returned the answer , ¯. Here the comma is a decimal separator. Here the comma is a decimal separator. Infix notation is a method similar to immediate execution with AESH and/or AESP, but unary operations are input into the calculator in the same order as they are written on paper.
If the biased sample variance (the second central moment of the sample, which is a downward-biased estimate of the population variance) is used to compute an estimate of the population's standard deviation, the result is = = (¯).
The total variation distance (or half the norm) arises as the optimal transportation cost, when the cost function is (,) =, that is, ‖ ‖ = (,) = {(): =, =} = [], where the expectation is taken with respect to the probability measure on the space where (,) lives, and the infimum is taken over all such with marginals and , respectively.