Algorithm Alley
by John C. Gunther

Listing One
ewInitialize(ew, alpha, firstData) {
  assert(0 <= alpha < 1)
  ew.alpha = alpha
  ew.average = firstData
}
ewUpdate(ew, newData) {  
  ew.average = ew.alpha*ew.average + (1-ew.alpha)*newData
}

Listing Two
ewInitialize(ew, alpha) {
  assert(0 <= alpha < 1)  
  ew.previousTime =  - INFINITY 
  ew.alpha = alpha
}
ewUpdate(ew, newData, time) {  
  weightReductionFactor  =  ew.alpha^(time - ew.previousTime)
  newDataWeight = 1 - weightReductionFactor
  ew.previousTime = time

  ew.average = weightReductionFactor * ew.average + newDataWeight*newData
}


Listing Three
ewInitialize(ew, alpha) {
  assert(0 <= alpha < 1)  
  ew.sumOfWeights = 0
  ew.sumOfData = 0
  ew.previousTime =  - INFINITY 
  ew.alpha = alpha
  ew.newDataWeightUpperBound = 1 - alpha
}
ewUpdate(ew, newData, time) {  
  assert (time > ew.previousTime)
  weightReductionFactor  =  ew.alpha^(time - ew.previousTime)
  newDataWeight = min(1 - weightReductionFactor, ew.newDataWeightUpperBound)
  ew.previousTime = time

  ew.sumOfWeights = weightReductionFactor* ew.sumOfWeights + newDataWeight
  ew.sumOfData = weightReductionFactor * ew.sumOfData + newDataWeight*newData

  ew.average = ew.sumOfData / ew.sumOfWeights
}

Listing Four
ewInitialize(ew, alpha, maxDt) {
  assert(0 <= alpha < 1)  
  assert(maxDt > 0)
  ew.sumOfWeights = 0
  ew.sumOfData = 0
  ew.sumOfSquaredData = 0  
  ew.previousTime =  - INFINITY 
  ew.alpha = alpha
  ew.newDataWeightUpperBound = 1 - alpha^maxDt 
}
ewUpdate(ew, newData, time) {  
  assert (time > ew.previousTime)
  weightReductionFactor  =  ew.alpha^(time - ew.previousTime)
  newDataWeight = min(1 - weightReductionFactor, ew.newDataWeightUpperBound)
  ew.sumOfWeights = weightReductionFactor* ew.sumOfWeights + newDataWeight
  ew.sumOfData = weightReductionFactor * ew.sumOfData + newDataWeight*newData
  ew.sumOfSquaredData = 
      weightReductionFactor* ew.sumOfSquaredData + newDataWeight*newData^2
  ew.previousTime = time
}
ewCompletenessFraction(ew, time) { 
  assert (time >= ew.previousTime)
  return(ew.alpha^(time - ew.previousTime) * ew.sumOfWeights) 
}
ewAverage(ew) {
  assert (ew.sumOfWeights > 0)
  return(ew.sumOfData/ew.sumOfWeights) 
}
ewStdDev(ew) {       
  assert (ew.sumOfWeights > 0)
  return(Sqrt(ew.sumOfSquaredData/ew.sumOfWeights  - ewAverage(ew)^2))
}


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