# mxnet.np.random.gumbel¶

gumbel(loc=0.0, scale=1.0, size=None, device=None, out=None)

Draw samples from a Gumbel distribution.

Draw samples from a Gumbel distribution with specified location and scale.

Parameters
• loc (float or array_like of floats, optional) – The location of the mode of the distribution. Default is 0.

• scale (float or array_like of floats, optional) – The scale parameter of the distribution. Default is 1. Must be non- negative.

• size (int or tuple of ints, optional) – Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if loc and scale are both scalars. Otherwise, np.broadcast(loc, scale).size samples are drawn.

• device (Device, optional) – Device context of output, default is current device.

• out (ndarray, optional) – Store output to an existing ndarray.

Returns

out – Drawn samples from the parameterized Gumbel distribution.

Return type

ndarray or scalar

Examples

Draw samples from the distribution: >>> mu, beta = 0, 0.1 # location and scale >>> s = np.random.gumbel(mu, beta, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, density=True) >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) … * np.exp( -np.exp( -(bins - mu) /beta) ), … linewidth=2, color=’r’) >>> plt.show() Show how an extreme value distribution can arise from a Gaussian process and compare to a Gaussian: >>> means = [] >>> maxima = [] >>> for i in range(0,1000) : … a = np.random.normal(mu, beta, 1000) … means.append(a.mean()) … maxima.append(a.max()) >>> count, bins, ignored = plt.hist(maxima, 30, density=True) >>> beta = np.std(maxima) * np.sqrt(6) / np.pi >>> mu = np.mean(maxima) - 0.57721*beta >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) … * np.exp(-np.exp(-(bins - mu)/beta)), … linewidth=2, color=’r’) >>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi)) … * np.exp(-(bins - mu)**2 / (2 * beta**2)), … linewidth=2, color=’g’) >>> plt.show()