samplingVarEst (version 1.4)

Pk.PropNorm.U: Inclusion probabilities proportional to a specified variable.

Description

Creates and normalises the 1st order inclusion probabilities proportional to a specified variable. In the current context, normalisation means that the inclusion probabilities are less than or equal to 1. Ideally, they should sum up to \(n\), the sample size.

Usage

Pk.PropNorm.U(n, VecMOS.U)

Value

The function returns a vector of length \(n\) with the inclusion probabilities.

Arguments

n

the sample size. It must be an integer or a double-precision scalar with zero-valued fractional part.

VecMOS.U

vector of the variable called measure of size (MOS) to which the first-order inclusion probabilities are to be proportional; its length is equal to the population size. Values in VecMOS.U should be greater than zero (a warning message appears if this does not hold). There must not be missing values.

Author

Emilio Lopez Escobar.

Details

Although the normalisation procedure is well-known in the survey sampling literature, we follow the procedure described in Chao (1982, p. 654). Hence, we obtain a unique set of inclusion probabilities that are proportional to the MOS variable.

References

Chao, M. T. (1982) A general purpose unequal probability sampling plan. Biometrika 69, 653--656.

See Also

Pkl.Hajek.s
Pkl.Hajek.U

Examples

data(oaxaca) #Loads the Oaxaca municipalities dataset
             #Creates the normalised 1st order incl. probs. proportional
             #to the variable oaxaca$HOMES00 and with sample size 373
pik.U <- Pk.PropNorm.U(373, oaxaca$HOMES00)
sum(pik.U)   #Shows the sum is equal to the sample size 373
any(pik.U>1) #Shows there isn't any probability greater than 1
any(pik.U<0) #Shows there isn't any probability less than 0