cent_sums {fromo}

Centered sums; join and unjoined.

Description

Compute, join, or unjoin centered sums.

Usage

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)

Arguments

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.

Value

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.

Note

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.

Author(s)

Steven E. Pav [e-mail]

References

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

Examples

 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)