var_st {stratallo} | R Documentation |
Variance of the Stratified Estimator
Description
Compute the value of the variance function of the stratified
estimator, which is of the following generic form:
where denotes total number of strata,
are strata
sample sizes and
, are population
constants.
Usage
var_st(x, A, A0)
var_st_tsi(x, N, S)
Arguments
x |
( |
A |
( |
A0 |
( |
N |
( |
S |
( |
Value
Value of the variance for a given allocation vector
.
Functions
-
var_st_tsi()
: computes value of variancefor the case of stratified
estimator of the population total and stratified simple random sampling without replacement design. This particular case yields:
where
is the size of stratum
, and
is stratum standard deviation of a study variable,
.
References
Särndal, C.-E., Swensson, B. and Wretman, J. (1992). Model Assisted Survey Sampling, Chapter 3.7 Stratified Sampling, Springer, New York.
Examples
N <- c(3000, 4000, 5000, 2000)
S <- rep(1, 4)
M <- c(100, 90, 70, 80)
xopt <- opt(n = 190, A = N * S, M = M)
var_st_tsi(x = xopt, N, S) # 1017579