var_tst

var_tst_si

<a href="https://lifecycle.r-lib.org/articles/stages.html#stable"><img src="figures/lifecycle-stable.svg?package=stratallo&version=2.1.0" alt="[Stable]"></a>
Compute the variance of the stratified pi-estimator of the population total,
that is of the following generic form:
$$D(x_1,...,x_H) = a^2_1/x_1 + ... + a^2_H/x_H - b,$$
where $H$ denotes total number of strata, $x_1, ..., x_H$ are the
strata sample sizes, and $b$, $a_w &gt; 0$ do not depend on
$x_w, w = 1, ..., H$.

Functions in this package provide solution to classical problem in
survey methodology - an optimum sample allocation in stratified sampling
schemes. In this context, the optimal allocation is in the classical
Tschuprov-Neyman's sense and it satisfies additional lower or upper bounds
restrictions imposed on sample sizes in strata. There are few different
algorithms available to use, and one them is based on popular sample
allocation method that applies Neyman allocation to recursively reduced set of
strata.
This package also provides the function that computes a solution to the minimum
sample size allocation problem, which is a minor modification of the classical
optimium sample allocation. This problem lies in the determination of a vector
of strata sample sizes that minimizes total sample size, under assumed fixed
level of the pi-estimator's variance. As in the case of the classical optimal
allocation, the problem of minimum sample size allocation can be complemented
by imposing upper bounds constraints on sample sizes in strata.

Wojciech Wojciak

stratallo

Optimum Sample Allocation in Stratified Sampling Schemes

Wojciech Wójciak

Jacek Wesołowski

Robert Wieczorkowski

var_tst function

<dl><dt>x</dt>
<dd>(<code>numeric</code>) sample allocations in strata. Strictly positive
numbers.</dd>
<dt>a</dt>
<dd>(<code>numeric</code>) parameters $a_1, ..., a_H$ of variance function
$D$. Strictly positive numbers.</dd>
<dt>b</dt>
<dd>(<code>numeric</code>) parameter $b$ of variance function $D$.</dd>
<dt>N</dt>
<dd>(<code>numeric</code>) strata sizes. Strictly positive numbers.</dd>
<dt>S</dt>
<dd>(<code>numeric</code>) strata standard deviations of a given study variable.
Strictly positive numbers.</dd></dl>

Arguments

<ul>
<li><code>var_tst_si</code>: computes variance of stratified pi-estimator of the total
for simple random sampling without replacement design in each stratum.
Under this design, parameters of the variance function $D$ take the
following form:
$$a_w = N_w * S_w, w = 1, ..., H,$$
and
$$b = N_1 * S_1^2 + ... + N_H * S_H^2,$$
where $N_w, S_w, w = 1, ..., H$, are strata sizes and standard
deviations of a study variable in strata respectively.</li>
</ul>

Functions

<a href='https://lifecycle.r-lib.org/articles/stages.html#stable'><img src='figures/lifecycle-stable.svg' alt='[Stable]' /></a>
Compute the variance of the stratified pi-estimator of the population total,
that is of the following generic form:
$$D(x_1,...,x_H) = a^2_1/x_1 + ... + a^2_H/x_H - b,$$
where $H$ denotes total number of strata, $x_1, ..., x_H$ are the
strata sample sizes, and $b$, $a_w &gt; 0$ do not depend on
$x_w, w = 1, ..., H$.

Variance of Stratified Pi-estimator of the Total — var_tst

<dl>

<dt>x</dt>
<dd>(<code>numeric</code>) sample allocations in strata. Strictly positive
numbers.</dd>


<dt>a</dt>
<dd>(<code>numeric</code>) parameters $a_1, ..., a_H$ of variance function
$D$. Strictly positive numbers.</dd>


<dt>b</dt>
<dd>(<code>numeric</code>) parameter $b$ of variance function $D$.</dd>


<dt>N</dt>
<dd>(<code>numeric</code>) strata sizes. Strictly positive numbers.</dd>


<dt>S</dt>
<dd>(<code>numeric</code>) strata standard deviations of a given study variable.
Strictly positive numbers.</dd>

</dl>

var_tst: Variance of Stratified Pi-estimator of the Total

Description

Usage

Value

Arguments

Functions

References

Examples