Computes cumulants up to some given order, then employs the Cornish-Fisher approximation to compute approximate quantiles using a Gaussian basis.
running_apx_quantiles(
v,
p,
window = NULL,
wts = NULL,
max_order = 5L,
na_rm = FALSE,
min_df = 0L,
used_df = 0,
restart_period = 100L,
check_wts = FALSE,
normalize_wts = TRUE,
check_negative_moments = TRUE
)running_apx_median(
v,
window = NULL,
wts = NULL,
max_order = 5L,
na_rm = FALSE,
min_df = 0L,
used_df = 0,
restart_period = 100L,
check_wts = FALSE,
normalize_wts = TRUE,
check_negative_moments = TRUE
)
A matrix, with one row for each element of x, and one column for each element of q.
a vector
the probability points at which to compute the quantiles. Should be in the range (0,1).
the window size. if given as finite integer or double, passed through.
If NULL, NA_integer_, NA_real_ or Inf are given, equivalent
to an infinite window size. If negative, an error will be thrown.
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.
the maximum order of the centered moment to be computed.
whether to remove NA, false by default.
the minimum df to return a value, otherwise NaN is returned.
This can be used to prevent moments from being computed on too few observations.
Defaults to zero, meaning no restriction.
the number of degrees of freedom consumed, used in the denominator of the centered moments computation. These are subtracted from the number of observations.
the recompute period. because subtraction of elements can cause loss of precision, the computation of moments is restarted periodically based on this parameter. Larger values mean fewer restarts and faster, though less accurate results.
a boolean for whether the code shall check for negative weights, and throw an error when they are found. Default false for speed.
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.
a boolean flag. Normal computation of running
moments can result in negative estimates of even order moments due to loss of
numerical precision. With this flag active, the computation checks for negative
even order moments and restarts the computation when one is detected. This
should eliminate the possibility of negative even order moments. The
downside is the speed hit of checking on every output step. Note also the
code checks for negative moments of every even order tracked, even if they
are not output; that is if the kurtosis, say, is being computed, and a
negative variance is detected, then the computation is restarted.
Defaults to TRUE to avoid negative even moments. Set to FALSE
only if you know what you are doing.
Steven E. Pav shabbychef@gmail.com
Computes the cumulants, then approximates quantiles using AS269 of Lee & Lin.
Terriberry, T. "Computing Higher-Order Moments Online." https://web.archive.org/web/20140423031833/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. tools:::Rd_expr_doi("10.1109/CLUSTR.2009.5289161")
Cook, J. D. "Accurately computing running variance." https://www.johndcook.com/standard_deviation/
Cook, J. D. "Comparing three methods of computing standard deviation." https://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation/
t_running_apx_quantiles, running_cumulants, PDQutils::qapx_cf, PDQutils::AS269.
x <- rnorm(1e5)
xq <- running_apx_quantiles(x,c(0.1,0.25,0.5,0.75,0.9))
xm <- running_apx_median(x)
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