wtd.moments {PracTools} | R Documentation |
Compute moments of a variable from either a population or sample
Description
Compute the 2nd, 3rd, 4th moments, skewness, and kurtosis of a variable from either population or sample input
Usage
wtd.moments(y, w=NULL, pop.sw=TRUE)
Arguments
y |
variable to be analyzed |
w |
vector of weights if the input is a sample |
pop.sw |
is the input for a population ( |
Details
The r^{th}
population moment is defined as m_r = (1/N) \sum_{k \in U} (y_k - \bar{y}_U)^r
where U is the set of population units, N is the population size, and \bar{y}_U
is the population mean. When the input is for the whole population, wtd.moments
evaluates this directly for r=2, 3, 4
. When the input is for a sample, the r^{th}
moment is estimated as \hat{m}_r = (K/\hat{N}) \sum_{k \in s} ( w_k (y_k - \hat{\bar{y}}_U)^r ), r=2, 3, 4
where s
is the set of sample units, w_k
is the weight for sample unit k
, \hat{N} = \sum_s w_k
, and \hat{\bar{y}}_U = \sum_{k \in s} w_k y_k / \hat{N}
. When r=2
, K=n/(n-1)
so that the estimator equals the unbiased variance estimator if the sample is a simple random sample; if r=3,4
, then K=1
. The function also computes or estimates the population skewness, defined as m_3/m_2^{3/2}
and the population kurtosis, m_4/m_2^2
.
The weights should be scaled for estimating population totals. The sample can be obtained from any complex design.
Value
Vector with values:
m2 |
2nd moment |
m3 |
3rd moment |
m4 |
4th moment |
skewness |
skewness |
kurtosis |
kurtosis |
Author(s)
Richard Valliant, Jill A. Dever, Frauke Kreuter
References
Valliant, R., Dever, J., Kreuter, F. (2018, sect. 3.4). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.
See Also
Examples
require(PracTools)
wtd.moments(y = hospital$y, w = NULL)
require(sampling)
sam <- strata(data = labor, stratanames = "h", size = c(30, 20, 10), method = c("srswor"),
description=TRUE)
samdat <- labor[sam$ID_unit,]
wtd.moments(y = samdat$WklyWage, w = 1/sam$Prob, pop.sw=FALSE)