T1T2.Mean.Var {RSizeBiased} | R Documentation |
Test statistic T_{n,r}^1
or T_{n,r}^2
depending on user input.
Description
The test statistics T_{n,r}^1
and T_{n,r}^2
are consistent estimators of the mean value \mathrm{E}(X)
and variance \mathrm{Var}(X)
respectively given an r-
size biased sample.
Usage
T1T2.Mean.Var(datain,r, type)
Arguments
datain |
The available sample points. |
r |
The size (order) of the distribution. The special cases |
type |
Numeric switch: type =1 corresponds to the T1 statistic while any other numeric value will cause calculation of T2. |
Details
The test statistic T_{n,r}^1
is defined by
T_{n,r}^{1}=\frac{\sum_{i=1}^n X_i^{1-r}}{\sum_{i=1}^n X_i^{-r}}.
The test statistic T_{n,r}^2
is defined by
T_{n,r}^{2}= \frac{\sum_{i=1}^n X_i^{2-r}}{\sum_{i=1}^nX_i^{-r}}-{\left(\frac{\sum_{i=1}^n X_i^{1-r}}{\sum_{i=1}^n X_i^{-r}}\right)^2}.
Value
A scalar, the value of the test statistic for the given sample.
Author(s)
Polychronis Economou
R implementation and documentation: Polychronis Economou <peconom@upatras.gr>
References
Economou et. al. (2021). Hypothesis testing for the population mean and variance based on r-size biased samples, under review.
Examples
#e.g.:
T1T2.Mean.Var(rgamma(100, 2,3),0, 1)