# Module: Distribution::NormalMultivariate

Defined in:
lib/distribution/normalmultivariate.rb

## Overview

Calculate cdf and inverse cdf for Multivariate Distribution.

## Class Method Summary collapse

• Returns multivariate cdf distribution * a is the array of lower values * b is the array of higher values * s is an symmetric positive definite covariance matrix.

## Class Method Details

### .cdf(aa, bb, sigma, epsilon = 0.0001, alpha = 2.5, max_iterations = 100) ⇒ Object

Returns multivariate cdf distribution

• a is the array of lower values
• b is the array of higher values
• s is an symmetric positive definite covariance matrix
 ``` 9 10 11 12 13 14 15 16 17 18 19 20 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 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62``` ```# File 'lib/distribution/normalmultivariate.rb', line 9 def cdf(aa, bb, sigma, epsilon = 0.0001, alpha = 2.5, max_iterations = 100) # :nodoc: fail "Doesn't work yet" a = [nil] + aa b = [nil] + bb m = aa.size sigma = sigma.to_gsl if sigma.respond_to? :to_gsl cc = GSL::Linalg::Cholesky.decomp(sigma) c = cc.lower intsum = 0 varsum = 0 n = 0 d = Array.new(m + 1, nil) e = Array.new(m + 1, nil) f = Array.new(m + 1, nil) (1..m).each do|i| d[i] = 0.0 if a[i].nil? e[i] = 1.0 if b[i].nil? end d[1] = uPhi(a[1].quo(c[0, 0])) unless d[1] == 0 e[1] = uPhi(b[1].quo(c[0, 0])) unless e[1] == 1 f[1] = e[1] - d[1] error = 1000 begin w = (m + 1).times.collect { |_i| rand * epsilon } y = [] (2..m).each do |i| y[i - 1] = iPhi(d[i - 1] + w[i - 1] * (e[i - 1] - d[i - 1])) sumc = 0 (1..(i - 1)).each do |j| sumc += c[i - 1, j - 1] * y[j] end d[i] = uPhi((a[i] - sumc).quo(c[i - 1, i - 1])) unless a[i].nil? # puts "sumc:#{sumc}" unless b[i].nil? # puts "e[#{i}] :#{c[i-1,i-1]}" e[i] = uPhi((b[i] - sumc).quo(c[i - 1, i - 1])) end f[i] = (e[i] - d[i]) * f[i - 1] end intsum += intsum + f[m] varsum += f[m]**2 n += 1 error = alpha * Math.sqrt((varsum.quo(n) - (intsum.quo(n))**2).quo(n)) end while(error > epsilon && n < max_iterations) f = intsum.quo(n) # p intsum # puts "f:#{f}, n:#{n}, error:#{error}" f end```

### .iPhi(pr) ⇒ Object

 ``` 64 65 66``` ```# File 'lib/distribution/normalmultivariate.rb', line 64 def iPhi(pr) Distribution::Normal.p_value(pr) end```

### .uPhi(x) ⇒ Object

 ``` 68 69 70``` ```# File 'lib/distribution/normalmultivariate.rb', line 68 def uPhi(x) Distribution::Normal.cdf(x) end```