Tail-Detection

Sample size n 72
Ahmad AU² (optimal) 0.136
p-Value for choosen parameter set 0.785 (calculated with 5000 MC steps)
Start of the Tail at datapoint k* 7
Tail weight k*/n 9.7%
Threshold u 27.6

Goodness-of-Fit Tests

Cramér-von Mises (p-Value) 0.04 (0.817)
Anderson-Darling (p-Value) 0.377 (0.686)

Fit Values

Generalized Pareto Distribution with location parameter zero

ξ σ
0.144 8.96

Risk assessment

Quantile Value-at-Risk
0.95 33.9
0.99 51.7
0.9999 132.9
Quantile Conditional-Value-at-Risk
0.95 50.0
0.99 70.9
0.9999 165.7

Input data

Tail-Detection and Test-Statistics

Empirical Distribution