The plot above shows several Levy distributions using formulas provided in the Wikipedia article about them.
Its fairly easy to make function plots like this. Use the Tools | “Generate a reference table…” to generate x values:
then use ALTER, UPDATE and the MySQL Mathematical Functions to add a column and fill it in with function values:
ALTER TABLE ref1
ADD COLUMN y double;
SET @c = 1.0;
UPDATE ref1
SET y = SQRT(@c / (PI() * 2.0))
* (EXP(-@c/ (2.0 * x)))
/ (POW(x, 1.5 )) ;
Finally, do the plot:
PLOT SCATTER
X, RED LINE, DARK GREEN LINE, BLUE LINE
WITH
TITLE "Levy Distributions"
SCALE Y 0 1.0 0.25
FORMAT Y DECIMAL "#.##"
SCALE Y2 0 1.0 0.25
NO LABELS Y2
TICKS X2 LEFT
SCALE X 0 3.0 1.0
SCALE X2 0 3.0 1.0
NO LABELS X2
TICKS X2 BOTTOM
LIGHT GRAY GRID LINES
LEGEND BOTTOM
SELECT
x,
y AS "c = 0.5",
y2 AS "c = 1.0",
y3 AS "c = 2.0"
FROM ref1;