2.3 Lower bound of SF for well-known distributions

Using numerical optimization [9, 10], for most of the top-fitted distributions from the maximum log likelihood approach, we get the minimum SF values, with distribution definition in [11] whose naming and parameterization for probability distributions will be used throughout this chapter, in Table 2.

From this table, we know that most of the distributions are not able to describe NATH since NATH has SF 1.834. More involved numerical integration and optimization also eliminated the Beckmann Distribution [12], with admissible SF range

#### Figure 3.

SF1 contour plot of Beta distribution. The horizontal axis is α and the vertical axis is β.
