exponentially smoothed moving average and variance

a.cr

class ExpMovingStats
  def initialize(@alpha : Float32)
    @mean = 0.0
    @variance = 0.0
  end

  def update(n)
    n = n.to_f32
    beta = 1.0 - @alpha

    @variance = beta * (@variance + (@alpha * ((n - @mean)**2)))
    @mean = (beta * @mean) + (@alpha * n)
  end

  def inspect(io : IO)
    io << "alpha:#{@alpha}\t"
    io << "mean: #{@mean.to_s.ljust(18)}\t"
    # io << "variance: #{@variance.to_s.ljust(18)}\t"
    io << "std: #{Math.sqrt(@variance)}"
  end
end

struct ManyAlphas
  property a1, a5, a9

  def initialize
    @a0 = ExpMovingStats.new(0.01)
    @a1 = ExpMovingStats.new(0.1)
    @a5 = ExpMovingStats.new(0.5)
    @a9 = ExpMovingStats.new(0.9)
  end

  def update(n)
    @a0.update(n)
    @a1.update(n)
    @a5.update(n)
    @a9.update(n)
  end

  def report
    p @a0
    p @a1
    p @a5
    p @a9
    puts
  end
end

A = ManyAlphas.new

def add(b, count)
  puts "#{b} added #{count} times"
  count.times { A.update(b + rand) }
  A.report
end

add 1, 60*60*3
add 10, 5
add 1, 60*60*24
add 60*2, 1
add 10, 5

output

> crystal a.cr
1 added 10800 times
alpha:0.01      mean: 1.5367347108387475        std: 0.2860789761362086
alpha:0.1       mean: 1.5858764719969363        std: 0.28348148931132433
alpha:0.5       mean: 1.725604657630973         std: 0.24601226582562175
alpha:0.9       mean: 1.8900307113084691        std: 0.13541845372467592

10 added 5 times
alpha:0.01      mean: 1.9623216071328642        std: 1.8957107711289498
alpha:0.1       mean: 5.127163855110824         std: 4.259336167806987
alpha:0.5       mean: 10.014975864573719        std: 1.4969537340305565
alpha:0.9       mean: 10.250793261568424        std: 0.09155541358114852

1 added 86400 times
alpha:0.01      mean: 1.4869804268745175        std: 0.27990040249991266
alpha:0.1       mean: 1.4671682770207035        std: 0.24949690662988483
alpha:0.5       mean: 1.4173783457309548        std: 0.14976189971229048
alpha:0.9       mean: 1.453421598422415         std: 0.08188044005780232

120 added 1 times
alpha:0.01      mean: 2.674269789274198         std: 11.816662449568861
alpha:0.1       mean: 13.342043587330135        std: 35.62541157596761
alpha:0.5       mean: 60.81664892017993         std: 59.39936369754038
alpha:0.9       mean: 108.33967050259999        std: 35.62876208816326

10 added 5 times
alpha:0.01      mean: 3.0624991976971128        std: 11.649790832586334
alpha:0.1       mean: 12.210285823347922        std: 27.409914231400048
alpha:0.5       mean: 12.091553195063073        std: 13.67063371425023
alpha:0.9       mean: 10.57956049215            std: 0.34997007299426763