94dea583-f4d2-4c12-9f22-85bf5ed2a6bd 21 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Note read first

This Smath document will help you complement the "Stat Treasury". 1. maple indefinite integral wiil solve for the cumulative CDF. 2. maple solve will solve for the quantile(s) ICDF. Most PDF from the treasury are already "normalised", i.e: the PDF are scaled to provide CDF from range(0..1)

α β x Fr_p α β / β x / (α 1 +^* β x / (α^- exp * :

α β x Fr_p x int maple α β x / ln * exp - exp

y α β x / ln * exp - exp ≡ x solve maple β y ln - ln α / exp /

α β x Fr_c α β x / ln * exp - exp :

α β x Fr_q β x ln - ln α / exp / :

PDF 0.5 1 x Fr_p 11 x Fr_p 21 x Fr_p 51 x Fr_p 41 sys :

CDF 0.5 1 x Fr_c 11 x Fr_c 21 x Fr_c 51 x Fr_c 41 sys :

QDF 0.5 1 x Fr_q 11 x Fr_q 21 x Fr_q 51 x Fr_q 41 sys :

Fréchet PDF "probability distribution"

PDF

Fréchet QDF "quantile"

QDF

Fréchet CDF "cumulative distribution"

CDF

Filling a statistical region [PDF]

Prepare the project

Construct the project

x f 51 x Fr_p :

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

sx 0.75 :

N 1000 :

xmin 0.75 :

xmax 1.5 :

ymin 0 :

ymax 2 :

space_x xmax xmin - (:

PDF x 1012 -^2 0.005 range : i 1 x rows range y i el x i el f eval : 11 line for x y augment 31 line :

space_y ymax ymin - (:

A function that tests an arbitrary point 
for its membership in the critical region. x y Test y x f ≤ (x xmax ≤ (* :

A routine that finds an array of N random 
pairs in the critical region. Pts i 1 N range x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 1 x y Test - x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 21 line while P i 1 el x : P i 2 el y : 51 line for P 21 line :

a b c spec . 7 #808080 13 mat :

fill Pts a b c spec pts :

Domain

Xmin xmin 1 xmin 0.25 - 22 mat :

Xmax xmax 1 xmax 0.25 - 22 mat :

Filling a range of a PDF

PDF Xmin Xmax fill 4 1 sys x f x xmin ≥ ( x xmax ≤ ( * / Xmin Xmax 3 1 sys

a xmin : b xmax : 21 line

x f x a b int 0.861827897942007

51 b Fr_c 51 a Fr_c - 0.861827896719184

f a b Int x f x a b int 32 / b a - (* w G w 01 int * ≡ memo ≡ w s b a - (34 / 2 w * 1 - (* 14 / 2 w * 1 - (3^* - 12 / + (* a + : w G w s f 12 w * 1 - (2^- (* : 32 / b a - (* w G w 01 int * 41 line :

f a b Int 0.861827894670677