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Estimate standard deviation using samples.

Given N samples of scalar valued random variable X, standard deviation may be estimated as

Stddev[X] := Sqrt[Var[X]],
Var[X] := N^{-1} sum_{n=1}^N (X_n - Xbar) Conj{(X_n - Xbar)},
Xbar := N^{-1} sum_{n=1}^N X_n
x = tf.random_normal(shape=(100, 2, 3))

# stddev[i, j] is the sample standard deviation of the (i, j) batch member.
stddev = tfp.stats.stddev(x, sample_axis=0)

Scaling a unit normal by a standard deviation produces normal samples with that standard deviation.

observed_data = read_data_samples(...)
stddev = tfp.stats.stddev(observed_data)

# Make fake_data with the same standard deviation as observed_data.
fake_data = stddev * tf.random_normal(shape=(100,))

Notice we divide by N (the numpy default), which does not create NaN when N = 1, but is slightly biased.


  • x: A numeric Tensor holding samples.
  • sample_axis: Scalar or vector Tensor designating axis holding samples, or None (meaning all axis hold samples). Default value: 0 (leftmost dimension).
  • keepdims: Boolean. Whether to keep the sample axis as singletons.
  • name: Python str name prefixed to Ops created by this function. Default value: None (i.e., 'stddev').


  • stddev: A Tensor of same dtype as the x, and rank equal to rank(x) - len(sample_axis)