T1T2.Mean.Var: Test statistic T_{n,r}^1 or T_{n,r}^2 depending on user...

In RSizeBiased: Hypothesis Testing Based on R-Size Biased Samples

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 r=1,2,3 correspond to length, area, volume biased samples respectively and are the most frequently encountered in practice. The case r=0 corresponds to random samples from the underlying distribution.
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{∑_{i=1}^n X_i^{1-r}}{∑_{i=1}^n X_i^{-r}}.

The test statistic T_{n,r}^2 is defined by

T_{n,r}^{2}= \frac{∑_{i=1}^n X_i^{2-r}}{∑_{i=1}^nX_i^{-r}}-{≤ft(\frac{∑_{i=1}^n X_i^{1-r}}{∑_{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 <[e-mail]>

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)

RSizeBiased documentation built on March 29, 2021, 9:11 a.m.