Therefore, motivated by the Pickands-Balkema-de Haan theorem, which states that losses that exceed a high threshold roughly follow a generalized Pareto distribution
, we use a two-component spliced distribution with the log-normal distribution fitting the data in the normal range and a generalized Pareto distribution
in the extreme range.
Note that the generalized Pareto distribution
implies the demand functions for sellers on the platform are defined by the class of demands with constant curvature of inverse demand (6)
Analyzing these results, according to Figure 3, it is possible to state that the location parameter could be represented by a Generalized Pareto distribution
scale parameter and the shape parameter could be represented by GEV distribution.
The density function can be deduced from generalized Pareto distribution
and log-likelihood function  is expressed as
Goodness-of-fit for the generalized Pareto distribution
. Technometrics, 43(4), 478-484.
Goodness-of-fit tests for the generalized Pareto distribution
. Technometrics, 43, 478-484.
The generalized Pareto distribution
in the extreme value theory has played an important role in modeling the excess distribution over a high threshold.
The defects can be solved by generalized Pareto distribution
(GPD) ("as discussed by Ashkar and El Adlouni ").
Generalized Logistic distribution (GLO), Generalized Pareto Distribution
(GPA) and Generalized Extreme Value distributions (GEV) are included in this study whose parameters are estimated by the method of L-moments and TL-moments.
They suggested that a generalized Pareto distribution
(GPD) is to be fitted, with the use of the Peaks- Over-Threshold (POT) method, to a dataset of residuals from an AR-GARCH filtering process.
where k [not equal to] 0 and probability density function for the three parameters generalized Pareto distribution
Areas for further study would include the use other ARMA-GARCH type models together with the use of a generalized Pareto distribution
or a generalized single Pareto distribution to estimate extreme tail quantiles.