Module: Distribution::T::Ruby_

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

Class Method Summary collapse

Class Method Details

.cdf(t, n) ⇒ Object

Returns the integral of t-distribution with n degrees of freedom over (-Infty, x].



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# File 'lib/distribution/t/ruby.rb', line 10

def cdf(t, n)
  p_t(n, t)
end

.p_t(df, t) ⇒ Object

t-distribution ([1]) (-infty, x]



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# File 'lib/distribution/t/ruby.rb', line 16

def p_t(df, t)
  if df.to_i!=df
    x=(t+Math.sqrt(t**2+df)) / (2*Math.sqrt(t**2+df))
    return Math.regularized_beta(x,df/2.0,df/2.0)
  end
  df=df.to_i
  c2 = df.to_f / (df + t * t);
  s = Math.sqrt(1.0 - c2)
  s = -s if t < 0.0
  p = 0.0;
  i = df % 2 + 2
  while i <= df
    p += s
    s *= (i - 1) * c2 / i
    i += 2
  end
  
  if df.is_a? Float or df & 1 != 0
    0.5+(p*Math.sqrt(c2)+Math.atan(t/Math.sqrt(df))) / Math::PI
  else
    (1.0 + p) / 2.0
  end
end

.p_value(y, n) ⇒ Object

Returns the P-value of tdist().



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# File 'lib/distribution/t/ruby.rb', line 99

def p_value(y,n)
  if y > 0.5
    pt(2.0 - y*2.0, n)
  else
    - pt(y*2.0, n)
  end
end

.pdf(t, v) ⇒ Object 



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# File 'lib/distribution/t/ruby.rb', line 5

def pdf(t,v)
  ((Math.gamma((v+1) / 2.0)) / (Math.sqrt(v*Math::PI)*Math.gamma(v/2.0))) * ((1+(t**2 / v.to_f))**(-(v+1) / 2.0))
  
end

.pt(q, n) ⇒ Object 



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# File 'lib/distribution/t/ruby.rb', line 67

def pt(q, n)
  q = q.to_f
  if(q < 1.0e-5 || q > 1.0 || n < 1)
  $stderr.printf("Error : Illegal parameter in pt()!\n")
  return 0.0
  end
  
  if(n <= 5) then return ptsub(q, n) end
  if(q <= 5.0e-3 && n <= 13) then return ptsub(q, n) end
  
  f1 = 4.0 * (f = n.to_f)
  f5 = (f4 = (f3 = (f2 = f * f) * f) * f) * f
  f2 *= 96.0
  f3 *= 384.0
  f4 *= 92160.0
  f5 *= 368640.0
  u = Normal.p_value(1.0 - q / 2.0)
  
  w0 = (u2 = u * u) * u
  w1 = w0 * u2
  w2 = w1 * u2
  w3 = w2 * u2
  w4 = w3 * u2
  w = (w0 + u) / f1
  w += (5.0 * w1 + 16.0 * w0 + 3.0 * u) / f2
  w += (3.0 * w2 + 19.0 * w1 + 17.0 * w0 - 15.0 * u) / f3
  w += (79.0 * w3 + 776.0 * w2 + 1482.0 * w1 - 1920.0 * w0 - 9450.0 * u) / f4
  w += (27.0 * w4 + 339.0 * w3 + 930.0 * w2 - 1782.0 * w1 - 765.0 * w0 + 17955.0 * u) / f5
  u + w
end

.ptsub(q, n) ⇒ Object

inverse of t-distribution ([2]) (-infty, -q/2] + [q/2, infty)



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# File 'lib/distribution/t/ruby.rb', line 43

def ptsub(q, n)
q = q.to_f
if(n == 1 && 0.001 < q && q < 0.01)
eps = 1.0e-4
elsif (n == 2 && q < 0.0001)
eps = 1.0e-4
elsif (n == 1 && q < 0.001)
eps = 1.0e-2
else
eps = 1.0e-5
end
s = 10000.0
w = 0.0
loop do
w += s
if(s <= eps) then return w end
if((qe = 2.0 - p_t(n, w)*2.0 - q) == 0.0) then return w end
if(qe < 0.0)
  w -= s
  s /= 10.0 #/
end
end
end