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The book's workers

The Chapter 4 example workers. A worker has the signature worker(rg, n, n_reps, param_tuple).

simstreams.workers

The book's example workers (Chapter 4).

A worker has the signature worker(rg, n, n_reps, param_tuple). It draws from rg, the process's own generator, generates data for n_reps replications of size n, computes the quantity of interest for each replication, and returns the results.

pi_worker 

pi_worker(rg, n, n_reps, param_tuple)

Estimate pi by dart throwing.

Each replication throws n uniform points at the square [-1, 1]^2 and estimates pi as four times the fraction that land inside the unit circle. param_tuple is unused.

Returns an array of n_reps estimates.

Source code in src/simstreams/workers.py 
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def pi_worker(rg, n, n_reps, param_tuple):
    """Estimate pi by dart throwing.

    Each replication throws ``n`` uniform points at the square [-1, 1]^2 and
    estimates pi as four times the fraction that land inside the unit circle.
    ``param_tuple`` is unused.

    Returns an array of ``n_reps`` estimates.
    """
    x = 2 * rg.random((n, n_reps)) - 1
    y = 2 * rg.random((n, n_reps)) - 1

    inside = x * x + y * y <= 1
    pi_hat = 4 * inside.mean(axis=0)

    return pi_hat

cauchy_worker 

cauchy_worker(rg, n, n_reps, param_tuple)

Estimate the Cauchy scale by half the interquartile range.

Each replication draws n observations from a Cauchy distribution with scale theta = param_tuple[0] by the quantile transformation and estimates the scale as half the sample interquartile range.

Returns an array of n_reps scale estimates.

Source code in src/simstreams/workers.py 
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def cauchy_worker(rg, n, n_reps, param_tuple):
    """Estimate the Cauchy scale by half the interquartile range.

    Each replication draws ``n`` observations from a Cauchy distribution with
    scale ``theta = param_tuple[0]`` by the quantile transformation and
    estimates the scale as half the sample interquartile range.

    Returns an array of ``n_reps`` scale estimates.
    """
    theta = param_tuple[0]

    U = rg.random((n, n_reps))
    X = theta * np.tan(np.pi * (U - 0.5))

    Q = np.quantile(X, [0.25, 0.75], axis=0)
    theta_hat = (Q[1] - Q[0]) / 2

    return theta_hat