Tail-Detection

Sample size n {{ data_size }}
Ahmad AU² (optimal) {{ au2_value|round(3) }}
p-Value for choosen parameter set {{ p_value_au2|round(3) }} (calculated with {{ montecarlo_steps }} MC steps)
Start of the Tail at datapoint k* {{ optimal_point_position }}
Tail weight k*/n {{ (optimal_point_position / data_size * 100)|round(1)}}%
Threshold u {{ optimal_point }}

Goodness-of-Fit Tests

Cramér-von Mises (p-Value) {{ w2_value|round(3) }} ({{ p_value_w2|round(3) }})
Anderson-Darling (p-Value) {{ a2_value|round(3) }} ({{ p_value_a2|round(3) }})

Fit Values

Generalized Pareto Distribution with location parameter zero

ξ σ
{{ fit_parameter.c|round(3) }} {{ fit_parameter.scale|round(3) }}

Risk assessment

{% for value in quantile %} {% endfor %}
Quantile Value-at-Risk
{{ value[0] }} {{ value[1] }}
{% for value in cond %} {% endfor %}
Quantile Conditional-Value-at-Risk
{{ value[0] }} {{ value[1] }}

Input data

Tail-Detection and Test-Statistics

Empirical Distribution