Estimate moments iteratively

In this example, we use the IterativeMoments class to compute iterative statistics. This class stores centered moments up to a prescribed order iteratively. Then several statistics based on the moments are available depending on the chosen order.

import openturns as ot
import openturns.viewer as otv

We first create a one-dimensional Gaussian random variable to generate data.

dim = 1
distNormal = ot.Normal(dim)

Then we use the centered moments up to order 4 with the IterativeMoments class by giving the order (here 4) and the dimension (here 1):

order = 4
iterMoments = ot.IterativeMoments(order, dim)

We can now perform the simulations. The IterativeMoments object stores the centered moments iteratively. We first increment the object with one Point at a time. At any given step the current mean is obtained thanks to the getMean() method and the current number of iterations is given by the getIterationNumber() method.

size = 2000
meanEvolution = ot.Sample()
for i in range(size):
    point = distNormal.getRealization()
    iterMoments.increment(point)
    meanEvolution.add(iterMoments.getMean())

We display the evolution of the mean.

iterationSample = ot.Sample.BuildFromPoint(range(1, size + 1))
curve = ot.Curve(iterationSample, meanEvolution)
graph = ot.Graph("Evolution of the mean", "iteration nb", "mean", True)
graph.add(curve)
graph.setLogScale(ot.GraphImplementation.LOGX)
view = otv.View(graph)

We can also increment with a Sample.

sample = distNormal.getSample(size)
iterMoments.increment(sample)

We print the total number of iterations and the mean.

print("Total number of iteration: ", iterMoments.getIterationNumber())
print("Mean: ", iterMoments.getMean())

Out:

Total number of iteration:  4000
Mean:  [-0.0137755]

For the order of the iterMoments object is 4, we also have access to other statistics such as the variance (order 2), the skewness (order 3) or the kurtosis (order 4). For instance, a specified order of 3 would leave only the variance and the skewness available.

print("Variance: ", iterMoments.getVariance())
print("Skewness: ", iterMoments.getSkewness())
print("Kurtosis: ", iterMoments.getKurtosis())

otv.View.ShowAll()

Out:

Variance:  [1.01255]
Skewness:  [0.00849145]
Kurtosis:  [3.02643]