1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
|
; test probability distributions and random number generators
; should do more extensive integration test
(setf eps 2.e-4)
(flet ((ptest (prob quant rand n &rest args)
(let* ((x (apply rand n args))
(x1 (apply quant (apply prob x args) args)))
(check #'< (abs (- x1 x)) (* eps (max (abs x)))))))
(ptest #'beta-cdf #'beta-quant #'beta-rand 20 2 3)
(ptest #'cauchy-cdf #'cauchy-quant #'cauchy-rand 20)
(ptest #'chisq-cdf #'chisq-quant #'chisq-rand 20 2)
(ptest #'gamma-cdf #'gamma-quant #'gamma-rand 20 5)
(ptest #'normal-cdf #'normal-quant #'normal-rand 20)
(ptest #'t-cdf #'t-quant #'t-rand 20 5)
(ptest #'identity #'identity #'uniform-rand 20)
(ptest #'f-cdf #'f-quant #'f-rand 20 2 3))
(labels ((trapezoid (from to n f args)
(let* ((x (rseq from to n))
(w (append '(.5) (repeat 1 (- n 2)) '(.5)))
(fvals (apply f x args)))
(* (/ (- to from) (- n 1))
(sum (* fvals w)))))
(int-test (dens quant &rest args)
(check #'<
(abs (- (trapezoid (apply quant .01 args)
(apply quant .99 args)
500
dens
args)
.98))
eps)))
(int-test #'beta-dens #'beta-quant 1.5 3)
(int-test #'cauchy-dens #'cauchy-quant)
(int-test #'chisq-dens #'chisq-quant 3)
(int-test #'gamma-dens #'gamma-quant 5)
(int-test #'normal-dens #'normal-quant)
(int-test #'t-dens #'t-quant 3)
(int-test #'f-dens #'f-quant 7 45))
|
