b979f73d-3ccf-45bd-b472-e57b53f0df9f

Build # b979f73d-3ccf-45bd-b472-e57b53f0df9f

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circleci

Committed by Enys Mones

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CodeScene badge updated

Pull Request Pull Request #63: Docs improvements

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97.75

/src/dist/noncentral-beta.js

import recursiveSum from '../algorithms/recursive-sum'
import { regularizedBetaIncomplete, beta as fnBeta, logGamma } from '../special'
import chi2 from './_chi2'
import noncentralChi2 from './_noncentral-chi2'
import Distribution from './_distribution'

/**
 * Generator for the [non-central beta distribution]{@link https://en.wikipedia.org/wiki/Noncentral_beta_distribution}:
 *
 * $$f(x; \alpha, \beta, \lambda) = e^{-\frac{\lambda}{2}} \sum\_{k = 0}^\infty \frac{1}{k!} \bigg(\frac{\lambda}{2}\bigg)^k \frac{x^{\alpha + k - 1} (1 - x)^{\beta - 1}}{\mathrm{B}(\alpha + k, \beta)},$$
 *
 * where $\alpha, \beta > 0$ and $\lambda \ge 0$. Support: $x \in \[0, 1\]$.
 *
 * @class NoncentralBeta
 * @memberof ran.dist
 * @param {number=} alpha First shape parameter. Default value is 1.
 * @param {number=} beta Second shape parameter. Default value is 1.
 * @param {number=} lambda Non-centrality parameter. Default value is 1.
 * @constructor
 */
export default class extends Distribution {
  // TODO Use outward iteration
  constructor (alpha = 1, beta = 1, lambda = 1) {
    super('continuous', arguments.length)

    // Validate parameters.
    this.p = { alpha, beta, lambda }
    Distribution.validate({ alpha, beta, lambda }, [
      'alpha > 0',
      'beta > 0',
      'lambda >= 0'
    ])

    // Set support.
    this.s = [{
      value: 0,
      closed: true
    }, {
      value: 1,
      closed: true
    }]

    // Speed-up constants.
    this.c = [
      Math.exp(-lambda / 2),
      fnBeta(alpha, beta)
    ]
  }

  _generator () {
    // Direct sampling from non-central chi2 and chi2.
    const x = noncentralChi2(this.r, 2 * this.p.alpha, this.p.lambda)
    const y = chi2(this.r, 2 * this.p.beta)
    const z = x / (x + y)

    // Handle 1 - z << 1 case.
    if (Math.abs(1 - z) < Number.EPSILON) {
      return 1 - y / x
    } else {
      return z
    }
  }

  _pdf (x) {
    // Speed-up variables.
    const l2 = this.p.lambda / 2
    const i0 = Math.round(l2)
    let iAlpha0 = this.p.alpha + i0

    // Init variables.
    const p0 = Math.exp(-l2 + i0 * Math.log(l2) - logGamma(i0 + 1))
    const xa0 = Math.pow(x, iAlpha0 - 1)
    const xb = Math.pow(1 - x, this.p.beta - 1)
    const b0 = fnBeta(iAlpha0, this.p.beta)

    // Forward sum.
    let z = recursiveSum({
      p: p0,
      xa: xa0,
      b: b0
    }, (t, i) => {
      t.p *= l2 / (i + i0)
      return t
    }, t => t.p * t.xa * xb / t.b, (t, i) => {
      const iAlpha = iAlpha0 + i
      t.xa *= x
      t.b *= iAlpha / (iAlpha + this.p.beta)
      return t
    })

    // Backward sum.
    if (i0 > 0) {
      iAlpha0--
      const xa = xa0 / x
      const b = b0 * (iAlpha0 + this.p.beta) / iAlpha0
      z += recursiveSum({
        p: p0 * i0 / l2,
        xa,
        b
      }, (t, i) => {
        const j = i0 - i - 1
        const iAlpha = iAlpha0 - i
        if (j >= 0) {
          t.p /= l2 / (j + 1)
          t.xa /= x
          t.b /= iAlpha / (iAlpha + this.p.beta)
        } else {
          t.p = 0
          t.ib = 0
        }
        return t
      }, t => t.p * t.xa * xb / t.b)
    }

    return z
  }

  _cdf (x) {
    // Speed-up variables
    const l2 = this.p.lambda / 2
    const i0 = Math.round(l2)
    let iAlpha0 = this.p.alpha + i0

    // Init variables
    const p0 = Math.exp(-l2 + i0 * Math.log(l2) - logGamma(i0 + 1))
    const xa0 = Math.pow(x, iAlpha0)
    const xb = Math.pow(1 - x, this.p.beta)
    const b0 = fnBeta(iAlpha0, this.p.beta)
    const ib0 = regularizedBetaIncomplete(iAlpha0, this.p.beta, x)

    // Forward sum.
    let z = recursiveSum({
      p: p0,
      xa: xa0,
      b: b0,
      ib: ib0
    }, (t, i) => {
      t.p *= l2 / (i + i0)
      return t
    }, t => t.p * t.ib, (t, i) => {
      const iAlpha = iAlpha0 + i
      t.ib -= t.xa * xb / (iAlpha * t.b)
      t.xa *= x
      t.b *= iAlpha / (iAlpha + this.p.beta)
      return t
    })

    // Backward sum.
    if (i0 > 0) {
      iAlpha0--
      const xa = xa0 / x
      const b = b0 * (iAlpha0 + this.p.beta) / iAlpha0
      z += recursiveSum({
        p: p0 * i0 / l2,
        xa,
        b,
        ib: ib0 + xa * xb / (iAlpha0 * b)
      }, (t, i) => {
        const j = i0 - i - 1
        const iAlpha = iAlpha0 - i
        if (j >= 0) {
          t.p /= l2 / (j + 1)
          t.xa /= x
          t.b /= iAlpha / (iAlpha + this.p.beta)
          t.ib += t.xa * xb / (iAlpha * t.b)
        } else {
          t.p = 0
          t.ib = 0
        }
        return t
      }, t => t.p * t.ib)
    }

    return Math.min(1, z)
  }
}

1	import recursiveSum from '../algorithms/recursive-sum'
2	import { regularizedBetaIncomplete, beta as fnBeta, logGamma } from '../special'
3	import chi2 from './_chi2'
4	import noncentralChi2 from './_noncentral-chi2'
5	import Distribution from './_distribution'
6
7	/**
8	* Generator for the [non-central beta distribution]{@link https://en.wikipedia.org/wiki/Noncentral_beta_distribution}:
9	*
10	* $$f(x; \alpha, \beta, \lambda) = e^{-\frac{\lambda}{2}} \sum\_{k = 0}^\infty \frac{1}{k!} \bigg(\frac{\lambda}{2}\bigg)^k \frac{x^{\alpha + k - 1} (1 - x)^{\beta - 1}}{\mathrm{B}(\alpha + k, \beta)},$$
11	*
12	* where $\alpha, \beta > 0$ and $\lambda \ge 0$. Support: $x \in \[0, 1\]$.
13	*
14	* @class NoncentralBeta
15	* @memberof ran.dist
16	* @param {number=} alpha First shape parameter. Default value is 1.
17	* @param {number=} beta Second shape parameter. Default value is 1.
18	* @param {number=} lambda Non-centrality parameter. Default value is 1.
19	* @constructor
20	*/
21	export default class extends Distribution {
22	// TODO Use outward iteration
23	constructor (alpha = 1, beta = 1, lambda = 1) {	84✔
24	super('continuous', arguments.length)	112✔
25
26	// Validate parameters.
27	this.p = { alpha, beta, lambda }	112✔
28	Distribution.validate({ alpha, beta, lambda }, [	112✔
29	'alpha > 0',
30	'beta > 0',
31	'lambda >= 0'
32	])
33
34	// Set support.
35	this.s = [{	102✔
36	value: 0,
37	closed: true
38	}, {
39	value: 1,
40	closed: true
41	}]
42
43	// Speed-up constants.
44	this.c = [	102✔
45	Math.exp(-lambda / 2),
46	fnBeta(alpha, beta)
47	]
48	}
49
50	_generator () {
51	// Direct sampling from non-central chi2 and chi2.
52	const x = noncentralChi2(this.r, 2 * this.p.alpha, this.p.lambda)	75,080✔
53	const y = chi2(this.r, 2 * this.p.beta)	75,080✔
54	const z = x / (x + y)	75,080✔
55
56	// Handle 1 - z << 1 case.
57	if (Math.abs(1 - z) < Number.EPSILON) {	75,080!
58	return 1 - y / x	×
59	} else {
60	return z	75,080✔
61	}
62	}
63
64	_pdf (x) {
65	// Speed-up variables.
66	const l2 = this.p.lambda / 2	529✔
67	const i0 = Math.round(l2)	529✔
68	let iAlpha0 = this.p.alpha + i0	529✔
69
70	// Init variables.
71	const p0 = Math.exp(-l2 + i0 * Math.log(l2) - logGamma(i0 + 1))	529✔
72	const xa0 = Math.pow(x, iAlpha0 - 1)	529✔
73	const xb = Math.pow(1 - x, this.p.beta - 1)	529✔
74	const b0 = fnBeta(iAlpha0, this.p.beta)	529✔
75
76	// Forward sum.
77	let z = recursiveSum({	529✔
78	p: p0,
79	xa: xa0,
80	b: b0
81	}, (t, i) => {
82	t.p *= l2 / (i + i0)	7,793✔
83	return t	7,793✔
84	}, t => t.p * t.xa * xb / t.b, (t, i) => {	8,322✔
85	const iAlpha = iAlpha0 + i	7,793✔
86	t.xa *= x	7,793✔
87	t.b *= iAlpha / (iAlpha + this.p.beta)	7,793✔
88	return t	7,793✔
89	})
90
91	// Backward sum.
92	if (i0 > 0) {	529✔
93	iAlpha0--	431✔
94	const xa = xa0 / x	431✔
95	const b = b0 * (iAlpha0 + this.p.beta) / iAlpha0	431✔
96	z += recursiveSum({	431✔
97	p: p0 * i0 / l2,
98	xa,
99	b
100	}, (t, i) => {
101	const j = i0 - i - 1	464✔
102	const iAlpha = iAlpha0 - i	464✔
103	if (j >= 0) {	464✔
104	t.p /= l2 / (j + 1)	33✔
105	t.xa /= x	33✔
106	t.b /= iAlpha / (iAlpha + this.p.beta)	33✔
107	} else {
108	t.p = 0	431✔
109	t.ib = 0	431✔
110	}
111	return t	464✔
112	}, t => t.p * t.xa * xb / t.b)	895✔
113	}
114
115	return z	529✔
116	}
117
118	_cdf (x) {
119	// Speed-up variables
120	const l2 = this.p.lambda / 2	67,121✔
121	const i0 = Math.round(l2)	67,121✔
122	let iAlpha0 = this.p.alpha + i0	67,121✔
123
124	// Init variables
125	const p0 = Math.exp(-l2 + i0 * Math.log(l2) - logGamma(i0 + 1))	67,121✔
126	const xa0 = Math.pow(x, iAlpha0)	67,121✔
127	const xb = Math.pow(1 - x, this.p.beta)	67,121✔
128	const b0 = fnBeta(iAlpha0, this.p.beta)	67,121✔
129	const ib0 = regularizedBetaIncomplete(iAlpha0, this.p.beta, x)	67,121✔
130
131	// Forward sum.
132	let z = recursiveSum({	67,121✔
133	p: p0,
134	xa: xa0,
135	b: b0,
136	ib: ib0
137	}, (t, i) => {
138	t.p *= l2 / (i + i0)	900,071✔
139	return t	900,071✔
140	}, t => t.p * t.ib, (t, i) => {	967,192✔
141	const iAlpha = iAlpha0 + i	900,071✔
142	t.ib -= t.xa * xb / (iAlpha * t.b)	900,071✔
143	t.xa *= x	900,071✔
144	t.b *= iAlpha / (iAlpha + this.p.beta)	900,071✔
145	return t	900,071✔
146	})
147
148	// Backward sum.
149	if (i0 > 0) {	67,121✔
150	iAlpha0--	63,163✔
151	const xa = xa0 / x	63,163✔
152	const b = b0 * (iAlpha0 + this.p.beta) / iAlpha0	63,163✔
153	z += recursiveSum({	63,163✔
154	p: p0 * i0 / l2,
155	xa,
156	b,
157	ib: ib0 + xa * xb / (iAlpha0 * b)
158	}, (t, i) => {
159	const j = i0 - i - 1	77,273✔
160	const iAlpha = iAlpha0 - i	77,273✔
161	if (j >= 0) {	77,273✔
162	t.p /= l2 / (j + 1)	14,110✔
163	t.xa /= x	14,110✔
164	t.b /= iAlpha / (iAlpha + this.p.beta)	14,110✔
165	t.ib += t.xa * xb / (iAlpha * t.b)	14,110✔
166	} else {
167	t.p = 0	63,163✔
168	t.ib = 0	63,163✔
169	}
170	return t	77,273✔
171	}, t => t.p * t.ib)	140,436✔
172	}
173
174	return Math.min(1, z)	67,121✔
175	}
176	}

synesenom / ran / b979f73d-3ccf-45bd-b472-e57b53f0df9f

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