centsums: Centered sums; join and unjoined.
In shabbychef/fromo: Fast Robust Moments

Description Usage Arguments Value Note Author(s) References Examples

Compute, join, or unjoin centered sums.

cent_sums(v, max_order = 5L, na_rm = FALSE, wts = NULL,
  check_wts = FALSE, normalize_wts = TRUE)

join_cent_sums(ret1, ret2)

unjoin_cent_sums(ret3, ret2)

`v`	a vector
`max_order`	the maximum order of the centered moment to be computed.
`na_rm`	whether to remove NA, false by default.
`wts`	an optional vector of weights. Weights are ‘replication’ weights, meaning a value of 2 is shorthand for having two observations with the corresponding `v` value. If `NULL`, corresponds to equal unit weights, the default. Note that weights are typically only meaningfully defined up to a multiplicative constant, meaning the units of weights are immaterial, with the exception that methods which check for minimum df will, in the weighted case, check against the sum of weights. For this reason, weights less than 1 could cause `NA` to be returned unexpectedly due to the minimum condition. When weights are `NA`, the same rules for checking `v` are applied. That is, the observation will not contribute to the moment if the weight is `NA` when `na_rm` is true. When there is no checking, an `NA` value will cause the output to be `NA`.
`check_wts`	a boolean for whether the code shall check for negative weights, and throw an error when they are found. Default false for speed.
`normalize_wts`	a boolean for whether the weights should be renormalized to have a mean value of 1. This mean is computed over elements which contribute to the moments, so if `na_rm` is set, that means non-NA elements of `wts` that correspond to non-NA elements of the data vector.
`ret1`	an ord+1 vector as output by `cent_sums` consisting of the count, the mean, then the k through ordth centered sum of some observations.
`ret2`	an ord+1 vector as output by `cent_sums` consisting of the count, the mean, then the k through ordth centered sum of some observations.
`ret3`	an ord+1 vector as output by `cent_sums` consisting of the count, the mean, then the k through ordth centered sum of some observations.

a vector the same size as the input consisting of the adjusted version of the input. When there are not sufficient (non-nan) elements for the computation, NaN are returned.

The moment computations provided by fromo are numerically robust, but will often not provide the same results as the 'standard' implementations, due to differences in roundoff. We make every attempt to balance speed and robustness. User assumes all risk from using the fromo package.

Steven E. Pav shabbychef@gmail.com

Terriberry, T. "Computing Higher-Order Moments Online." http://people.xiph.org/~tterribe/notes/homs.html

J. Bennett, et. al., "Numerically Stable, Single-Pass, Parallel Statistics Algorithms," Proceedings of IEEE International Conference on Cluster Computing, 2009. https://www.semanticscholar.org/paper/Numerically-stable-single-pass-parallel-statistics-Bennett-Grout/a83ed72a5ba86622d5eb6395299b46d51c901265

Cook, J. D. "Accurately computing running variance." http://www.johndcook.com/standard_deviation.html

Cook, J. D. "Comparing three methods of computing standard deviation." http://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation

 set.seed(1234)
 x1 <- rnorm(1e3,mean=1)
 x2 <- rnorm(1e3,mean=1)
 max_ord <- 6L
 rs1 <- cent_sums(x1,max_ord)
 rs2 <- cent_sums(x2,max_ord)
 rs3 <- cent_sums(c(x1,x2),max_ord)
 rs3alt <- join_cent_sums(rs1,rs2)
 stopifnot(max(abs(rs3 - rs3alt)) < 1e-7)
 rs1alt <- unjoin_cent_sums(rs3,rs2)
 rs2alt <- unjoin_cent_sums(rs3,rs1)
 stopifnot(max(abs(rs1 - rs1alt)) < 1e-7)
 stopifnot(max(abs(rs2 - rs2alt)) < 1e-7)