# LognormalQQ: Log-normal quantile plot In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

 LognormalQQ R Documentation

## Log-normal quantile plot

### Description

Computes the empirical quantiles of the log-transform of a data vector and the theoretical quantiles of the standard normal distribution. These quantiles are then plotted in a log-normal QQ-plot with the theoretical quantiles on the x-axis and the empirical quantiles on the y-axis.

### Usage

LognormalQQ(data, plot = TRUE, main = "Log-normal QQ-plot", ...)

### Arguments

 data Vector of n observations. 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

By definition, a log-transformed log-normal random variable is normally distributed. We can thus obtain a log-normal QQ-plot from a normal QQ-plot by replacing the empirical quantiles of the data vector by the empirical quantiles from the log-transformed data. We hence plot

(\Phi^{-1}(i/(n+1)), \log(X_{i,n}) )

for i=1,\ldots,n, where \Phi is the standard normal CDF.

See Section 4.1 of Albrecher et al. (2017) for more details.

### Value

A list with following components:

 lnqq.the Vector of the theoretical quantiles from a standard normal distribution. lnqq.emp Vector of the empirical quantiles from the log-transformed data.

Tom Reynkens.

### References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

Beirlant J., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.

ExpQQ, ParetoQQ, WeibullQQ

### Examples

data(norwegianfire)

# Log-normal QQ-plot for Norwegian Fire Insurance data for claims in 1976.
LognormalQQ(norwegianfire\$size[norwegianfire\$year==76])

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