Module: Distribution::ChiSquare::Ruby_

Extended by:
Math
Defined in:
lib/distribution/chisquare/ruby.rb

Class Method Summary collapse

• CDF Inverse over [x, \infty) Pr([x, \infty)) = y -> x.

• chi-square distribution ([1]) Integral over [x, \infty).

• .quantile(pr, k) ⇒ Object (also: p_value)

Class Method Details

.cdf(x, k) ⇒ Object

 47 48 49 # File 'lib/distribution/chisquare/ruby.rb', line 47 def cdf(x, k) 1.0 - q_chi2(k, x) end

.pchi2(n, y) ⇒ Object

CDF Inverse over [x, \infty) Pr([x, \infty)) = y -> x

 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 # File 'lib/distribution/chisquare/ruby.rb', line 21 def pchi2(n, y) if n == 1 w = Distribution::Normal.p_value(1 - y / 2) # = p1.0-Distribution::Normal.cdf(y/2) w * w elsif n == 2 # v = (1.0 / y - 1.0) / 33.0 # newton_a(y, v) {|x| [q_chi2(n, x), -chi2dens(n, x)] } -2.0 * Math.log(y) else eps = 1.0e-5 v = 0.0 s = 10.0 loop do v += s break if s <= eps if (qe = q_chi2(n, v) - y) == 0.0 then break end if qe < 0.0 v -= s s /= 10.0 end end v end end

.pdf(x, n) ⇒ Object

 6 7 8 9 10 11 12 13 14 15 16 17 # File 'lib/distribution/chisquare/ruby.rb', line 6 def pdf(x, n) if n == 1 1.0 / Math.sqrt(2 * Math::PI * x) * Math::E**(-x / 2.0) elsif n == 2 0.5 * Math::E**(-x / 2.0) else n = n.to_f n2 = n / 2 x = x.to_f 1.0 / 2**n2 / gamma(n2) * x**(n2 - 1.0) * Math.exp(-x / 2.0) end end

.q_chi2(df, chi2) ⇒ Object

chi-square distribution ([1]) Integral over [x, \infty)

 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 # File 'lib/distribution/chisquare/ruby.rb', line 53 def q_chi2(df, chi2) chi2 = chi2.to_f if (df & 1) != 0 chi = Math.sqrt(chi2) return 2 * (1.0 - Distribution::Normal.cdf(chi)) if (df == 1) s = t = chi * Math.exp(-0.5 * chi2) / SQ2PI k = 3 while k < df t *= chi2 / k; s += t k += 2 end 2 * (1.0 - (Distribution::Normal.cdf(chi)) + s) else s = t = Math.exp(-0.5 * chi2) k = 2 while k < df t *= chi2 / k; s += t k += 2 end s end end

.quantile(pr, k) ⇒ ObjectAlso known as: p_value

 81 82 83 # File 'lib/distribution/chisquare/ruby.rb', line 81 def quantile(pr, k) pchi2(k, 1.0 - pr) end