@@ -4180,7 +4180,7 @@ def quantile(a,
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a : array_like of real numbers
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Input array or object that can be converted to an array.
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q : array_like of float
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- Probability or sequence of probabilities for the quantiles to compute.
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+ Probability or sequence of probabilities of the quantiles to compute.
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Values must be between 0 and 1 inclusive.
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axis : {int, tuple of int, None}, optional
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Axis or axes along which the quantiles are computed. The default is
@@ -4270,10 +4270,6 @@ def quantile(a,
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Given a sample `a` from an underlying distribution, `quantile` provides a
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nonparametric estimate of the inverse cumulative distribution function.
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- Sample quantiles, the result of ``quantile``, provide nonparametric
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- estimation of the underlying population counterparts, represented by the
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- unknown :math:`F`, given a data vector `a` of length ``n``.
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-
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By default, this is done by interpolating between adjacent elements in
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``y``, a sorted copy of `a`::
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@@ -4336,12 +4332,16 @@ def quantile(a,
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.. math:: P(Y < x) \\ leq q \\ quad\\ text{and}\\ quad P(Y \\ leq x) \\ geq q
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with random variable :math:`Y\\ sim P`.
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+ Sample quantiles, the result of `quantile`, provide nonparametric
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+ estimation of the underlying population counterparts, represented by the
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+ unknown :math:`F`, given a data vector `a` of length ``n``.
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+
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Some of the estimators above arise when one considers :math:`F` as the
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empirical distribution function of the data, i.e.
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:math:`F(y) = \\ frac{1}{n} \\ sum_i 1_{a_i \\ leq y}`.
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Then, different methods correspond to different choices of :math:`x` that
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- fulfill the above coverage conditions. Methods that follow this approach are
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- ``inverted_cdf`` and ``averaged_inverted_cdf``.
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+ fulfill the above coverage conditions. Methods that follow this approach
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+ are ``inverted_cdf`` and ``averaged_inverted_cdf``.
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For weighted quantiles, the coverage conditions still hold. The
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empirical cumulative distribution is simply replaced by its weighted
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