# cLognormalQQ: Log-normal quantile plot for right censored data In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

 cLognormalQQ R Documentation

## Log-normal quantile plot for right censored data

### Description

Log-normal QQ-plot adapted for right censored data.

### Usage

``````cLognormalQQ(data, censored, plot = TRUE, main = "Log-normal QQ-plot", ...)
``````

### Arguments

 `data` Vector of `n` observations. `censored` A logical vector of length `n` indicating if an observation is censored. `plot` Logical indicating if the quantiles should be plotted in a log-normal QQ-plot, default is `TRUE`. `main` Title for the plot, default is `"Log-normal QQ-plot"`. `...` Additional arguments for the `plot` function, see `plot` for more details.

### Details

The log-normal QQ-plot adapted for right censoring is given by

`( \Phi^{-1}(F_{km}(Z_{j,n})), \log(Z_{j,n}) )`

for `j=1,\ldots,n-1,` with `Z_{i,n}` the `i`-th order statistic of the data, `\Phi^{-1}` the quantile function of the standard normal distribution and `F_{km}` the Kaplan-Meier estimator for the CDF. Hence, it has the same empirical quantiles as an ordinary log-normal QQ-plot but replaces the theoretical quantiles ` \Phi^{-1}(j/(n+1))` by `\Phi^{-1}(F_{km}(Z_{j,n}))`.

This QQ-plot is only suitable for right censored data.

In Beirlant et al. (2007), only a Pareto QQ-plot adapted for right-censored data is proposed. This QQ-plot is constructed using the same ideas, but is not described in the paper.

### Value

A list with following components:

 `lqq.the` Vector of the theoretical quantiles, see Details. `lqq.emp` Vector of the empirical quantiles from the log-transformed data.

Tom Reynkens

### References

Beirlant, J., Guillou, A., Dierckx, G. and Fils-Villetard, A. (2007). "Estimation of the Extreme Value Index and Extreme Quantiles Under Random Censoring." Extremes, 10, 151–174.

`LognormalQQ`, `cExpQQ`, `cParetoQQ`, `cWeibullQQ`, `KaplanMeier`

### Examples

``````# Set seed
set.seed(29072016)

# Pareto random sample
X <- rpareto(500, shape=2)

# Censoring variable
Y <- rpareto(500, shape=1)

# Observed sample
Z <- pmin(X, Y)

# Censoring indicator
censored <- (X>Y)

# Log-normal QQ-plot adapted for right censoring
cLognormalQQ(Z, censored=censored)
``````

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.