235 lines
9.9 KiB
JavaScript
235 lines
9.9 KiB
JavaScript
|
var vows = require('vows');
|
||
|
|
var assert = require('assert');
|
||
|
|
var suite = vows.describe('jStat.distribution');
|
||
|
|
|
||
|
|
require('../env.js');
|
||
|
|
|
||
|
|
suite.addBatch({
|
||
|
|
'kumaraswamy pdf': {
|
||
|
|
'topic': function() {
|
||
|
|
return jStat;
|
||
|
|
},
|
||
|
|
// Checked against R's dkumar(p, shape1, shape2, log=FALSE) in package VGAM
|
||
|
|
// install.packages("VGAM")
|
||
|
|
// library("VGAM")
|
||
|
|
// options(digits=10)
|
||
|
|
// dkumar(c(-5, 5), 2, 2)
|
||
|
|
'check pdf calculation': function(jStat) {
|
||
|
|
var tol = 0.0000001;
|
||
|
|
// outside support
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(-5, 2, 2), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(5, 2, 2), 0);
|
||
|
|
}
|
||
|
|
},
|
||
|
|
'kumaraswamy inv': {
|
||
|
|
'topic': function() {
|
||
|
|
return jStat;
|
||
|
|
},
|
||
|
|
// Checked against R's
|
||
|
|
// qkumar(p, shape1, shape2, lower.tail=TRUE, log.p=FALSE) in package VGAM
|
||
|
|
// install.packages("VGAM")
|
||
|
|
// library("VGAM")
|
||
|
|
// options(digits=10)
|
||
|
|
// qkumar(c(0, 0.5, 1), 0.5, 0.5)
|
||
|
|
// qkumar(c(0, 0.5, 1), 0.8, 1)
|
||
|
|
// qkumar(c(0, 0.5, 1), 1, 0.4)
|
||
|
|
// qkumar(c(0, 0.5, 1), 0.6, 1.2)
|
||
|
|
// qkumar(c(0, 0.5, 1), 1, 1)
|
||
|
|
// qkumar(c(0, 0.5, 1), 2, 1)
|
||
|
|
// qkumar(c(0, 0.5, 1), 1.5, 1.5)
|
||
|
|
// qkumar(c(0, 0.5, 1), 7, 25)
|
||
|
|
'check inv calculation': function(jStat) {
|
||
|
|
var tol = 0.0000001;
|
||
|
|
// 'U'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0, 0.5, 0.5), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0.5, 0.5, 0.5), 0.5625);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(1, 0.5, 0.5), 1);
|
||
|
|
|
||
|
|
// 'L'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0, 0.8, 1), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0.5, 0.8, 1), 0.4204482076);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(1, 0.8, 1), 1);
|
||
|
|
|
||
|
|
// reversed-'L'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0, 1, 0.4), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0.5, 1, 0.4), 0.8232233047);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(1, 1, 0.4), 1);
|
||
|
|
|
||
|
|
// sideways-'S'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0, 0.6, 1.2), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0.5, 0.6, 1.2), 0.2533532737);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(1, 0.6, 1.2), 1);
|
||
|
|
|
||
|
|
// flat distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0, 1, 1), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0.5, 1, 1), 0.5);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(1, 1, 1), 1);
|
||
|
|
|
||
|
|
// '/'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0, 2, 1), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0.5, 2, 1), 0.7071067812);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(1, 2, 1), 1);
|
||
|
|
|
||
|
|
// inverted-'U'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0, 1.5, 1.5), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0.5, 1.5, 1.5), 0.5154248709);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(1, 1.5, 1.5), 1);
|
||
|
|
|
||
|
|
// peaked distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0, 7, 25), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(0.5, 7, 25), 0.5979941923);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.inv(1, 7, 25), 1);
|
||
|
|
}
|
||
|
|
},
|
||
|
|
|
||
|
|
'kumaraswamy pdf': {
|
||
|
|
'topic': function() {
|
||
|
|
return jStat;
|
||
|
|
},
|
||
|
|
// Checked against R's dkumar(p, shape1, shape2, log=FALSE) in package VGAM
|
||
|
|
// install.packages("VGAM")
|
||
|
|
// library("VGAM")
|
||
|
|
// options(digits=10)
|
||
|
|
// dkumar(c(0, 0.5, 1), 0.5, 0.5)
|
||
|
|
// dkumar(c(0, 0.5, 1), 0.8, 1) # Note: Incorrectly returns NaN for x = 1!
|
||
|
|
// dkumar(c(0, 0.5, 1), 1, 0.4) # Note: Incorrectly returns NaN for x = 0!
|
||
|
|
// dkumar(c(0, 0.5, 1), 0.6, 1.2)
|
||
|
|
// dkumar(c(0, 0.5, 1), 1.3, 0.5)
|
||
|
|
// dkumar(c(0, 0.5, 1), 1, 1) # Note: Incorrectly returns NaN for x = 0 and x = 1!
|
||
|
|
// dkumar(c(0, 0.5, 1), 2, 1) # Note: Incorrectly returns NaN for x = 1!
|
||
|
|
// dkumar(c(0, 0.5, 1), 1, 1.5) # Note: Incorrectly returns NaN for x = 0!
|
||
|
|
// dkumar(c(0, 0.5, 1), 1.5, 1.5)
|
||
|
|
// dkumar(c(0, 0.5, 1), 7, 25)
|
||
|
|
'check pdf calculation': function(jStat) {
|
||
|
|
var tol = 0.0000001;
|
||
|
|
// 'U'-shaped distribution
|
||
|
|
assert.equal(jStat.kumaraswamy.pdf(0, 0.5, 0.5), Infinity);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 0.5, 0.5), 0.6532814824);
|
||
|
|
assert.equal(jStat.kumaraswamy.pdf(1, 0.5, 0.5), Infinity);
|
||
|
|
|
||
|
|
// 'L'-shaped distribution
|
||
|
|
assert.equal(jStat.kumaraswamy.pdf(0, 0.8, 1), Infinity);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 0.8, 1), 0.918958684);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(1, 0.8, 1), 0.8);
|
||
|
|
|
||
|
|
// reversed-'L'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0, 1, 0.4), 0.4);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 1, 0.4), 0.6062866266);
|
||
|
|
assert.equal(jStat.kumaraswamy.pdf(1, 1, 0.4), Infinity);
|
||
|
|
|
||
|
|
// sideways-'S'-shaped distribution
|
||
|
|
assert.equal(jStat.kumaraswamy.pdf(0, 0.6, 1.2), Infinity);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 0.6, 1.2), 0.7657783992);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(1, 0.6, 1.2), 0);
|
||
|
|
|
||
|
|
// sideways-'Z'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0, 1.3, 0.5), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 1.3, 0.5), 0.6851052165);
|
||
|
|
assert.equal(jStat.kumaraswamy.pdf(1, 1.3, 0.5), Infinity);
|
||
|
|
|
||
|
|
// flat distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0, 1, 1), 1);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 1, 1), 1);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(1, 1, 1), 1);
|
||
|
|
|
||
|
|
// '/'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0, 2, 1), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 2, 1), 1);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(1, 2, 1), 2);
|
||
|
|
|
||
|
|
// '\'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0, 1, 1.5), 1.5);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 1, 1.5), 1.060660172);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(1, 1, 1.5), 0);
|
||
|
|
|
||
|
|
// inverted-'U'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0, 1.5, 1.5), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 1.5, 1.5), 1.279186452);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(1, 1.5, 1.5), 0);
|
||
|
|
|
||
|
|
// peaked distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0, 7, 25), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(0.5, 7, 25), 2.265208101);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.pdf(1, 7, 25), 0);
|
||
|
|
}
|
||
|
|
},
|
||
|
|
'kumaraswamy cdf': {
|
||
|
|
'topic': function() {
|
||
|
|
return jStat;
|
||
|
|
},
|
||
|
|
// Checked against R's pkumar(q, shape1, shape2, lower.tail = TRUE, log.p = FALSE) in package VGAM
|
||
|
|
// install.packages("VGAM")
|
||
|
|
// library("VGAM")
|
||
|
|
// options(digits=10)
|
||
|
|
// pkumar(c(0, 0.5, 1), 0.5, 0.5)
|
||
|
|
// pkumar(c(0, 0.5, 1), 0.8, 1) # Note: Incorrectly returns NaN for x = 1!
|
||
|
|
// pkumar(c(0, 0.5, 1), 1, 0.4) # Note: Incorrectly returns NaN for x = 0!
|
||
|
|
// pkumar(c(0, 0.5, 1), 0.6, 1.2)
|
||
|
|
// pkumar(c(0, 0.5, 1), 1.3, 0.5)
|
||
|
|
// pkumar(c(0, 0.5, 1), 1, 1) # Note: Incorrectly returns NaN for x = 0 and x = 1!
|
||
|
|
// pkumar(c(0, 0.5, 1), 2, 1) # Note: Incorrectly returns NaN for x = 1!
|
||
|
|
// pkumar(c(0, 0.5, 1), 1, 1.5) # Note: Incorrectly returns NaN for x = 0!
|
||
|
|
// pkumar(c(0, 0.5, 1), 1.5, 1.5)
|
||
|
|
// pkumar(c(0, 0.5, 1), 7, 25)
|
||
|
|
// pkumar(c(-5, 5), 2, 2)
|
||
|
|
'check cdf calculation': function(jStat) {
|
||
|
|
var tol = 0.0000001;
|
||
|
|
// 'U'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 0.5, 0.5), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 0.5, 0.5), 0.4588038999);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 0.5, 0.5), 1);
|
||
|
|
|
||
|
|
// 'L'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 0.8, 1), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 0.8, 1), 0.5743491775);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 0.8, 1), 1);
|
||
|
|
|
||
|
|
// reversed-'L'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 1, 0.4), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 1, 0.4), 0.2421417167);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 1, 0.4), 1);
|
||
|
|
|
||
|
|
// sideways-'S'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 0.6, 1.2), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 0.6, 1.2), 0.7257468009);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 0.6, 1.2), 1);
|
||
|
|
|
||
|
|
// sideways-'Z'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 1.3, 0.5), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 1.3, 0.5), 0.2293679206);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 1.3, 0.5), 1);
|
||
|
|
|
||
|
|
// flat distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 1, 1), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 1, 1), 0.5);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 1, 1), 1);
|
||
|
|
|
||
|
|
// '/'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 2, 1), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 2, 1), 0.25);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 2, 1), 1);
|
||
|
|
|
||
|
|
// '\'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 1, 1.5), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 1, 1.5), 0.6464466094);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 1, 1.5), 1);
|
||
|
|
|
||
|
|
// inverted-'U'-shaped distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 1.5, 1.5), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 1.5, 1.5), 0.4802446206);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 1.5, 1.5), 1);
|
||
|
|
|
||
|
|
// peaked distribution
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0, 7, 25), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(0.5, 7, 25), 0.1780530605);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(1, 7, 25), 1);
|
||
|
|
|
||
|
|
// outside support
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(-5, 2, 2), 0);
|
||
|
|
assert.epsilon(tol, jStat.kumaraswamy.cdf(5, 2, 2), 1);
|
||
|
|
}
|
||
|
|
},
|
||
|
|
});
|
||
|
|
|
||
|
|
suite.export(module);
|