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ReIns (version 1.0.7)

trTest: Test for truncated Pareto-type tails

Description

Test between non-truncated Pareto-type tails (light truncation) and truncated Pareto-type tails (rough truncation).

Usage

trTest(data, alpha = 0.05, plot = TRUE, main = "Test for truncation", ...)

Arguments

data

Vector of n observations.

alpha

The used significance level, default is 0.05.

plot

Logical indicating if the P-values should be plotted as a function of k, default is FALSE.

main

Title for the plot, default is "Test for truncation".

Additional arguments for the plot function, see plot for more details.

Value

A list with following components:

k

Vector of the values of the tail parameter k.

testVal

Corresponding test values.

critVal

Critical value used for the test, i.e. qnorm(1-alpha/2).

Pval

Corresponding P-values.

Reject

Logical vector indicating if the null hypothesis is rejected for a certain value of k.

Details

We want to test H0:X has non-truncated Pareto tails vs. H1:X has truncated Pareto tails. Let Ek,n(γ)=1/kj=1k(Xnk,n/Xnj+1,n)1/γ, with Xi,n the i-th order statistic. The test statistic is then Tk,n=12k(Ek,n(Hk,n)1/2)/(1Ek,n(Hk,n)) which is asymptotically standard normally distributed. We reject H0 on level α if Tk,n<zα where zα is the 100(1α)% quantile of a standard normal distribution. The corresponding P-value is thus given by Φ(Tk,n) with Φ the CDF of a standard normal distribution.

See Beirlant et al. (2016) or Section 4.2.3 of Albrecher et al. (2017) for more details.

References

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

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

trHill, trTestMLE

Examples

Run this code
# NOT RUN {
# Sample from truncated Pareto distribution.
# truncated at 95% quantile
shape <- 2
X <- rtpareto(n=1000, shape=shape, endpoint=qpareto(0.95, shape=shape))

# Test for truncation
trTest(X)


# Sample from truncated Pareto distribution.
# truncated at 99% quantile
shape <- 2
X <- rtpareto(n=1000, shape=shape, endpoint=qpareto(0.99, shape=shape))

# Test for truncation
trTest(X)
# }

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