Module: Distribution::Normal::Ruby_

Defined in:
lib/distribution/normal/ruby.rb

Class Method Summary (collapse)

Class Method Details

+ (Object) cdf(z)

Normal cumulative distribution function (cdf).

Returns the integral of normal distribution over (-Infty, z].



65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
# File 'lib/distribution/normal/ruby.rb', line 65

def cdf(z)
  0.0 if z < -12 
  1.0 if z > 12
  0.5 if z == 0.0 

  if z > 0.0
    e = true
  else
    e = false
    z = -z
  end
  z = z.to_f
  z2 = z * z
  t = q = z * Math.exp(-0.5 * z2) / SQ2PI

  3.step(199, 2) do |i|
    prev = q
    t *= z2 / i
    q += t
    if q <= prev
      return(e ? 0.5 + q : 0.5 - q)
    end
  end
  e ? 1.0 : 0.0
end

+ (Object) p_value(qn)

Return the inverse CDF or P-value of the corresponding integral



37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
# File 'lib/distribution/normal/ruby.rb', line 37

def p_value(qn)
  b = [1.570796288, 0.03706987906, -0.8364353589e-3,
  -0.2250947176e-3, 0.6841218299e-5, 0.5824238515e-5,
  -0.104527497e-5, 0.8360937017e-7, -0.3231081277e-8,
  0.3657763036e-10, 0.6936233982e-12]

  if(qn < 0.0 || 1.0 < qn)
  $stderr.printf("Error : qn <= 0 or qn >= 1  in pnorm()!\n")
  return 0.0;
  end
  qn == 0.5 and return 0.0

  w1 = qn
  qn > 0.5 and w1 = 1.0 - w1
  w3 = -Math.log(4.0 * w1 * (1.0 - w1))
  w1 = b[0]
  1.upto 10 do |i|
  w1 += b[i] * w3**i;
  end
  qn > 0.5 and return Math.sqrt(w1 * w3)
  -Math.sqrt(w1 * w3)

end

+ (Object) pdf(x)

Normal probability density function (pdf) With x=0 and sigma=1



93
94
95
# File 'lib/distribution/normal/ruby.rb', line 93

def pdf(x)
  (1.0 / SQ2PI)*Math::exp(-(x**2/2.0))
end

+ (Object) rng(mean = 0, sigma = 1, seed = nil)

Return a proc which return a random number within a gaussian distribution X ~ N(mean,sigma^2) seed feed the

Reference:



15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
# File 'lib/distribution/normal/ruby.rb', line 15

def rng(mean=0,sigma=1,seed=nil)
  returned,y1,y2=0,0,0
  lambda {
    if returned==0
      begin
        x1 = 2.0 * rand - 1.0
        x2 = 2.0 * rand - 1.0
        w = x1 * x1 + x2 * x2
      end while ( w >= 1.0 )
      w = Math::sqrt( (-2.0 * Math::log( w ) ) / w )
      y1 = x1 * w
      y2 = x2 * w
      returned=1
      y1*sigma + mean
    else
      returned=0
      y2 * sigma + mean
    end
  }

end

+ (Object) rngu

random number within a gaussian distribution X ~ N(0,1)



7
8
9
# File 'lib/distribution/normal/ruby.rb', line 7

def rngu
  rng(0,1,nil)
end