Johnson SU Distribution

The Johnson SU distribution is a flexible distribution that is derived from transformations to the normal distribution. It is especially useful for modeling data with unconventional shapes that would be difficult to capture with other distributions. This includes heavily skewed data or data with extremely long tails. Depending on how it is parameterized, the Johnson SU distribution can model both symmetric and asymmetric distributions.

The four parameters are as follows:

• Parameter 1 (γ or gamma) is the shape parameter that affects the skewness of the distribution.

  • A positive P1 will skew the distribution to the left, resulting in a longer left tail.

  • A negative P1 will skew the distribution to the right, resulting in a longer right tail.

• Parameter 2 (δ or delta) is a secondary shape parameter that affects the kurtosis of the distribution.

  • A smaller P2 will result in a lower peak and thicker tails.

  • A larger P2 will result in a higher peak and thinner tails.

• Parameter 3 (ξ or xi) is the location parameter that shifts the distribution along the x-axis.

  • A positive P3 will shift the distribution to the right.

  • A negative P3 will shift the distribution to the left.

• Parameter 4 (λ or lambda) is the scale parameter that can compress or stretch the distribution.

  • A smaller P4 decreases the spread of the distribution, effectively compressing it horizontally.

  • A larger P4 increases the spread of the distribution, effectively stretching it horizontally.