In the appendix, we repeat the simulation analysis but modify the assumption regarding the distribution of losses such that [X.sub.1], [X.sub.2], and [X.sub.3] follow a

Pareto distribution (Pareto(2, 1)).

For illustrative purposes, we assume that F takes on a simple

Pareto distribution(2014) for each sample year, to estimate the coefficient of a Type-I

Pareto distribution for earnings above the 99th percentile.

Pareto's discovery has since been called many names such as Pareto Principle, Pareto Law,

Pareto Distribution, Law of Least Effect, 80/rules, Principle of imbalance and 80/20 thinking (Koch, 2011a, 2011b, 2013).An expert and inordinate writer (Koch, 2011a, 2011b, 2013) in the field of Pareto Principle affirmed that the executives those who apply Pareto Principle in their duty takes enjoy more benefits or compensation whether public or private.

The thing that is interesting is that Pareto extended the 80/20 rules and developed the

Pareto Distribution.

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.

To determine the bilateral threshold levels and the index [V.sub.ij,t], a typical assumption is that the distribution of input requirement across firms is characterised by the

Pareto distribution. If the

Pareto distribution is untruncated (lower bound for the input requirement equals zero), [V.sub.ij,t] > 0 since some firms in i will have a low enough input requirement to export to j.

It should be emphasized here that many phenomena in both the natural and social sciences have power law statistics (

Pareto distribution).

The simple theory of optimal taxation that Diamond and Saez provide relies on the assumption that income among the top 1 percent is distributed according to the

Pareto distribution. Named after economist Vilfredo Pareto (1848-1923), it is a distribution that is known to have a thick (sometimes called a "fat") tail.

Goodness-of-fit for the generalized

Pareto distribution. Technometrics, 43(4), 478-484.

The

Pareto distribution is a compound Gaussian model with a Rayleigh distribution being modulated by an inverse Gamma distribution [25-27].