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#: ../../source/reference/tensor/generated/mars.tensor.random.gumbel.rst:2
msgid "mars.tensor.random.gumbel"
msgstr ""

#: mars.tensor.random.gumbel:1 of
msgid "Draw samples from a Gumbel distribution."
msgstr ""

#: mars.tensor.random.gumbel:3 of
msgid ""
"Draw samples from a Gumbel distribution with specified location and "
"scale.  For more information on the Gumbel distribution, see Notes and "
"References below."
msgstr ""

#: mars.tensor.random.gumbel of
msgid "Parameters"
msgstr ""

#: mars.tensor.random.gumbel:7 of
msgid "The location of the mode of the distribution. Default is 0."
msgstr ""

#: mars.tensor.random.gumbel:9 of
msgid "The scale parameter of the distribution. Default is 1."
msgstr ""

#: mars.tensor.random.gumbel:11 of
msgid ""
"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."
msgstr ""

#: mars.tensor.random.gumbel:16 of
msgid "Desired chunk size on each dimension"
msgstr ""

#: mars.tensor.random.gumbel:18 of
msgid "Allocate the tensor on GPU if True, False as default"
msgstr ""

#: mars.tensor.random.gumbel:20 of
msgid "Data-type of the returned tensor."
msgstr ""

#: mars.tensor.random.gumbel of
msgid "Returns"
msgstr ""

#: mars.tensor.random.gumbel:23 of
msgid "**out** -- Drawn samples from the parameterized Gumbel distribution."
msgstr ""

#: mars.tensor.random.gumbel of
msgid "Return type"
msgstr ""

#: mars.tensor.random.gumbel:26 of
msgid ""
":func:`scipy.stats.gumbel_l`, :func:`scipy.stats.gumbel_r`, "
":func:`scipy.stats.genextreme`, :func:`weibull`"
msgstr ""

#: mars.tensor.random.gumbel:29 of
msgid "Notes"
msgstr ""

#: mars.tensor.random.gumbel:30 of
msgid ""
"The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value"
" Type I) distribution is one of a class of Generalized Extreme Value "
"(GEV) distributions used in modeling extreme value problems. The Gumbel "
"is a special case of the Extreme Value Type I distribution for maximums "
"from distributions with \"exponential-like\" tails."
msgstr ""

#: mars.tensor.random.gumbel:36 of
msgid "The probability density for the Gumbel distribution is"
msgstr ""

#: mars.tensor.random.gumbel:38 of
msgid ""
"p(x) = \\frac{e^{-(x - \\mu)/ \\beta}}{\\beta} e^{ -e^{-(x - \\mu)/ "
"\\beta}},"
msgstr ""

#: mars.tensor.random.gumbel:41 of
msgid ""
"where :math:`\\mu` is the mode, a location parameter, and :math:`\\beta` "
"is the scale parameter."
msgstr ""

#: mars.tensor.random.gumbel:44 of
msgid ""
"The Gumbel (named for German mathematician Emil Julius Gumbel) was used "
"very early in the hydrology literature, for modeling the occurrence of "
"flood events. It is also used for modeling maximum wind speed and "
"rainfall rates.  It is a \"fat-tailed\" distribution - the probability of"
" an event in the tail of the distribution is larger than if one used a "
"Gaussian, hence the surprisingly frequent occurrence of 100-year floods. "
"Floods were initially modeled as a Gaussian process, which underestimated"
" the frequency of extreme events."
msgstr ""

#: mars.tensor.random.gumbel:53 of
msgid ""
"It is one of a class of extreme value distributions, the Generalized "
"Extreme Value (GEV) distributions, which also includes the Weibull and "
"Frechet."
msgstr ""

#: mars.tensor.random.gumbel:57 of
msgid ""
"The function has a mean of :math:`\\mu + 0.57721\\beta` and a variance of"
" :math:`\\frac{\\pi^2}{6}\\beta^2`."
msgstr ""

#: mars.tensor.random.gumbel:61 of
msgid "References"
msgstr ""

#: mars.tensor.random.gumbel:62 of
msgid ""
"Gumbel, E. J., \"Statistics of Extremes,\" New York: Columbia University "
"Press, 1958."
msgstr ""

#: mars.tensor.random.gumbel:64 of
msgid ""
"Reiss, R.-D. and Thomas, M., \"Statistical Analysis of Extreme Values "
"from Insurance, Finance, Hydrology and Other Fields,\" Basel: Birkhauser "
"Verlag, 2001."
msgstr ""

#: mars.tensor.random.gumbel:69 of
msgid "Examples"
msgstr ""

#: mars.tensor.random.gumbel:70 of
msgid "Draw samples from the distribution:"
msgstr ""

#: mars.tensor.random.gumbel:77 of
msgid ""
"Display the histogram of the samples, along with the probability density "
"function:"
msgstr ""

#: mars.tensor.random.gumbel:88 of
msgid ""
"Show how an extreme value distribution can arise from a Gaussian process "
"and compare to a Gaussian:"
msgstr ""

