Module: Statistics2

Defined in:
lib/statistics2.rb

Overview

statistics2.rb

distributions of statistics             
  by Shin-ichiro HARA

URL: blade.nagaokaut.ac.jp/~sinara/ruby/math/

2003.09.25

Ref:
  [1] http://www.matsusaka-u.ac.jp/~okumura/algo/
  [2] http://www5.airnet.ne.jp/tomy/cpro/sslib11.htm

Constant Summary collapse

SQ2PI =

:nodoc:

Math.sqrt(2 * Math::PI)
LOG_2PI =

Gamma function

Math.log(2 * Math::PI)
N = 
8
B0 = 
1.0
B1 = 
-1.0 / 2.0
B2 = 
1.0 / 6.0
B4 = 
-1.0 / 30.0
B6 = 
1.0 / 42.0
B8 = 
-1.0 / 30.0
B10 = 
5.0 / 66.0
B12 = 
-691.0 / 2730.0
B14 = 
7.0 / 6.0
B16 = 
-3617.0 / 510.0

Class Method Summary collapse

Class Method Details

.bin_x(n, p, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 514

def bin_x(n, p, x); bindist(n, 1.0 - p, n - x);  end

.bindens(n, p, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 435

def bindens(n, p, x)
  p = p.to_f
  q = 1.0 - p
  combi(n, x) * p**x * q**(n - x)
end

.bindist(n, p, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 441

def bindist(n, p, x)
  (0..x).inject(0.0) do |s, k|
    s + bindens(n, p, k)
  end
end

.binX_(n, p, x) ⇒ Object

discrete distributions



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# File 'lib/statistics2.rb', line 513

def binX_(n, p, x); bindist(n, p, x); end

.chi2_x(n, x) ⇒ Object

chi2-distribution



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# File 'lib/statistics2.rb', line 477

def chi2_x(n, x); 1.0 - chi2dist(n, x); end

.chi2dist(n, x) ⇒ Object

chi-square-distribution interface



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# File 'lib/statistics2.rb', line 215

def chi2dist(n, x); 1.0 - q_chi2(n, x); end

.chi2X_(n, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 478

def chi2X_(n, x); chi2dist(n, x); end

.f_x(n1, n2, x) ⇒ Object

F-distribution



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# File 'lib/statistics2.rb', line 503

def f_x(n1, n2, x); 1.0 - fdist(n1, n2, x); end

.fdist(n1, n2, f) ⇒ Object

F-distribution interface



409
 
# File 'lib/statistics2.rb', line 409

def fdist(n1, n2, f); 1.0 - q_f(n1, n2, f); end

.fX_(n1, n2, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 504

def fX_(n1, n2, x); fdist(n1, n2, x); end

.normal___x(z) ⇒ Object 



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# File 'lib/statistics2.rb', line 464

def normal___x(z); 1.0 - normaldist(z); end

.normal__X_(z) ⇒ Object 



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# File 'lib/statistics2.rb', line 463

def normal__X_(z); normaldist(z) - 0.5; end

.normaldist(z) ⇒ Object

normal-distribution interface



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# File 'lib/statistics2.rb', line 137

def normaldist(z)
  p_nor(z)
end

.normalx__x(z) ⇒ Object 



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# File 'lib/statistics2.rb', line 465

def normalx__x(z); 2.0 - normaldist(z) * 2.0; end

.normalxXX_(z) ⇒ Object

normal-distribution



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# File 'lib/statistics2.rb', line 462

def normalxXX_(z); normaldist(z); end

.pchi2_x(n, y) ⇒ Object

inverse of chi2-distribution



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# File 'lib/statistics2.rb', line 482

def pchi2_x(n, y); pchi2dist(n, 1.0 - y); end

.pchi2dist(n, y) ⇒ Object 



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# File 'lib/statistics2.rb', line 216

def pchi2dist(n, y); pchi2(n, 1.0 - y); end

.pchi2X_(n, y) ⇒ Object 



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# File 'lib/statistics2.rb', line 483

def pchi2X_(n, y); pchi2dist(n, y); end

.pf_x(n1, n2, x) ⇒ Object

inverse of F-distribution



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# File 'lib/statistics2.rb', line 508

def pf_x(n1, n2, x); pfdist(n1, n2, 1.0 - x); end

.pfdist(n1, n2, y) ⇒ Object 



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# File 'lib/statistics2.rb', line 410

def pfdist(n1, n2, y); pf(1.0 - y, n1, n2); end

.pfX_(n1, n2, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 509

def pfX_(n1, n2, x); pfdist(n1, n2, x); end

.pnormal___x(y) ⇒ Object 



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# File 'lib/statistics2.rb', line 471

def pnormal___x(y); pnormalxXX_(1.0 - y); end

.pnormal__X_(y) ⇒ Object 



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# File 'lib/statistics2.rb', line 470

def pnormal__X_(y); pnormalxXX_(y + 0.5); end

.pnormaldist(y) ⇒ Object 



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# File 'lib/statistics2.rb', line 141

def pnormaldist(y)
  pnorm(y)
end

.pnormalx__x(y) ⇒ Object 



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# File 'lib/statistics2.rb', line 472

def pnormalx__x(y); pnormalxXX_(1.0 - y/2.0); end

.pnormalxXX_(z) ⇒ Object

inverse of normal-distribution



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# File 'lib/statistics2.rb', line 469

def pnormalxXX_(z); pnormaldist(z); end

.poisson_x(m, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 518

def poisson_x(m, x); 1.0 - poissondist(m, x-1); end

.poissondens(m, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 447

def poissondens(m, x)
  return 0.0 if x < 0
  m = m.to_f
  m ** x * Math::E ** (-m) / perm(x)
end

.poissondist(m, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 453

def poissondist(m, x)
  (0..x).inject(0.0) do |s, k|
    s + poissondens(m, k)
  end
end

.poissonX_(m, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 517

def poissonX_(m, x); poissondist(m, x); end

.pt___x(n, y) ⇒ Object 



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# File 'lib/statistics2.rb', line 498

def pt___x(n, y); ptdist(n, 1.0 - y); end

.pt__X_(n, y) ⇒ Object 



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# File 'lib/statistics2.rb', line 497

def pt__X_(n, y); ptdist(n, 0.5 + y); end

.ptdist(n, y) ⇒ Object 



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# File 'lib/statistics2.rb', line 302

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

.ptx__x(n, y) ⇒ Object

inverse of t-distribution



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# File 'lib/statistics2.rb', line 495

def ptx__x(n, y); ptdist(n, 1.0 - y / 2.0); end

.ptxXX_(n, y) ⇒ Object 



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# File 'lib/statistics2.rb', line 496

def ptxXX_(n, y); ptdist(n, y); end

.t___x(n, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 491

def t___x(n, x); 1.0 - tdist(n, x); end

.t__X_(n, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 490

def t__X_(n, x); tdist(n, x) - 0.5; end

.tdist(n, t) ⇒ Object

t-distribution interface



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# File 'lib/statistics2.rb', line 301

def tdist(n, t); p_t(n, t); end

.tx__x(n, x) ⇒ Object

t-distribution



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# File 'lib/statistics2.rb', line 488

def tx__x(n, x); 2.0 - tdist(n, x) * 2.0; end

.txXX_(n, x) ⇒ Object 



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# File 'lib/statistics2.rb', line 489

def txXX_(n, x); tdist(n, x); end