zeta_plug_in: zeta_{n,r}^i, i=1,2 test statistic for the Weibull or the...
In RSizeBiased: Hypothesis Testing Based on R-Size Biased Samples

Description Usage Arguments Details Value Author(s) References Examples

View source: R/zeta_plug_in.R

Studentized version of the T^i_{n,r}, i=1,2 test statistic for the Weibull/gamma distribution.

1	zeta_plug_in(null_value, datain,r,EST_par,type, dist)

`null_value`	The parameter value in the hypothesis test under the null
`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.
`EST_par`	A vector of length 2, containing the shape and scale parameters of the Weibull distribution.
`type`	Numeric switch: type =1 returns the ζ_{n,r}^1 test statistic, any other value returns ζ_{n,r}^2
`dist`	Character switch, enables the choice of distribution: type "weib" for the Weibull or "gamma" for the gamma distribution.

When type=1 the function returns

√{n} \frac{T_{n,r^1} - μ^0}{ σ_{1,r}(\hat θ_n)} \rightarrow N(0,1)

after using the fact that under the null we have μ_1=μ^0. Any other value for type returns

√{n} \frac{T_{n,r^2} - σ_0^2}{ σ_{2,r}(\hat θ_n)} \rightarrow N(0,1)

in which case the fact that var(X)=σ_0^2 under the null has been used.

A scalar with the value of the test statistic.

Polychronis Economou

R implementation and documentation: Polychronis Economou <peconom@upatras.gr>

Economou et. al. (2021). Hypothesis testing for the population mean and variance based on r-size biased samples, under review.

data(ufc)
datain_r <- ufc[,4]
nullMEAN <- 14
# ml estimates = c(2.6555,8.0376),  taken from section 6.2 in Economou et. al. (2021).
zeta_plug_in(nullMEAN, datain_r, 2, c(2.6555,8.0376),1, "gamma") #corresponds to mean

nullVar <- 180
zeta_plug_in(nullVar, datain_r, 2, c(2.6555,8.0376),2, "gamma") #corresponds to var