trParetoQQ {ReIns} | R Documentation |
Truncated Pareto quantile plot
Description
Extension of the Pareto QQ-plot as described in Beirlant et al. (2016).
Usage
trParetoQQ(data, r = 1, DT, kstar = NULL, plot = TRUE, main = "TPa QQ-plot", ...)
Arguments
data |
Vector of |
r |
Trimming parameter, default is |
DT |
Vector of |
kstar |
Value for |
plot |
Logical indicating if the quantiles should be plotted in a Pareto QQ-plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
Details
The Pareto QQ-plot for truncated data plots
(-\log(\hat{D}_{T,r,k^*,n}+j/(n+1)), \log(X_{n-j+1,n}) )
for j=1,\ldots,n
.
The value for k^*
can be be given by the user or can be determined automatically.
In the latter case, we use the k^*
that maximises the absolute value of the correlation between -\log(\hat{D}_{T,r,k^*,n}+j/(n+1))
and \log(X_{n-j+1,n})
for j=1,\ldots,k
and k^*>10
.
When taking D_T=0
, one obtains the ordinary Pareto QQ-plot.
Note that the definition here differs slightly from the one in Beirlant et al. (2016). We plot the empirical and theoretical quantiles the other way around and therefore have to add a minus (before the log).
See Beirlant et al. (2016) for more details.
Value
A list with following components:
pqq.the |
Vector of theoretical quantiles |
pqq.emp |
Vector of the empirical quantiles from the log-transformed data. |
kstar |
Optimal value for |
DTstar |
Estimate of |
Author(s)
Tom Reynkens.
References
Beirlant, J., Fraga Alves, M.I. and Gomes, M.I. (2016). "Tail fitting for Truncated and Non-truncated Pareto-type Distributions." Extremes, 19, 429–462.
See Also
Examples
# Endpoint of truncated Pareto distribution
endpoint <- qpareto(0.99, shape=2)
# Generate sample from truncated Pareto distribution
X <- rtpareto(1000, shape=2, endpoint=endpoint)
# Ordinary Pareto QQ-plot
ParetoQQ(X)
# Truncated Hill estimates
gamma <- trHill(X)$gamma
# Estimates for truncation odds
dt <- trDT(X, gamma=gamma)$DT
# Truncated Pareto QQ-plot
trParetoQQ(X, DT=dt)