Python norm.ppf方法代码示例

# 需要导入模块: from scipy.stats.distributions import norm [as 别名]
# 或者: from scipy.stats.distributions.norm import ppf [as 别名]
def test_null_distribution():

    # Create a mixed population of Z-scores: 1000 standard normal and
    # 20 uniformly distributed between 3 and 4.
    grid = np.linspace(0.001, 0.999, 1000)
    z0 = norm.ppf(grid)
    z1 = np.linspace(3, 4, 20)
    zs = np.concatenate((z0, z1))
    emp_null = NullDistribution(zs, estimate_null_proportion=True)

    assert_allclose(emp_null.mean, 0, atol=1e-5, rtol=1e-5)
    assert_allclose(emp_null.sd, 1, atol=1e-5, rtol=1e-2)
    assert_allclose(emp_null.null_proportion, 0.98, atol=1e-5, rtol=1e-2)

    # consistency check
    assert_allclose(emp_null.pdf(np.r_[-1, 0, 1]),
                    norm.pdf(np.r_[-1, 0, 1], loc=emp_null.mean, scale=emp_null.sd),
                    rtol=1e-13) 

# 需要导入模块: from scipy.stats.distributions import norm [as 别名]
# 或者: from scipy.stats.distributions.norm import ppf [as 别名]
def test_local_fdr():

    # Create a mixed population of Z-scores: 1000 standard normal and
    # 20 uniformly distributed between 3 and 4.
    grid = np.linspace(0.001, 0.999, 1000)
    z0 = norm.ppf(grid)
    z1 = np.linspace(3, 4, 20)
    zs = np.concatenate((z0, z1))

    # Exact local FDR for U(3, 4) component.
    f1 = np.exp(-z1**2 / 2) / np.sqrt(2*np.pi)
    r = len(z1) / float(len(z0) + len(z1))
    f1 /= (1 - r) * f1 + r

    fdr = local_fdr(zs)
    fdr1 = fdr[len(z0):]

    assert_allclose(f1, fdr1, rtol=0.05, atol=0.1) 

# 需要导入模块: from scipy.stats.distributions import norm [as 别名]
# 或者: from scipy.stats.distributions.norm import ppf [as 别名]
def mquantiles_cimj(data, prob=[0.25,0.50,0.75], alpha=0.05, axis=None):
    """
    Computes the alpha confidence interval for the selected quantiles of the
    data, with Maritz-Jarrett estimators.

    Parameters
    ----------
    data : ndarray
        Data array.
    prob : sequence, optional
        Sequence of quantiles to compute.
    alpha : float, optional
        Confidence level of the intervals.
    axis : int or None, optional
        Axis along which to compute the quantiles.
        If None, use a flattened array.

    """
    alpha = min(alpha, 1-alpha)
    z = norm.ppf(1-alpha/2.)
    xq = mstats.mquantiles(data, prob, alphap=0, betap=0, axis=axis)
    smj = mjci(data, prob, axis=axis)
    return (xq - z * smj, xq + z * smj) 

# 需要导入模块: from scipy.stats.distributions import norm [as 别名]
# 或者: from scipy.stats.distributions.norm import ppf [as 别名]
def mquantiles_cimj(data, prob=[0.25,0.50,0.75], alpha=0.05, axis=None):
    """
    Computes the alpha confidence interval for the selected quantiles of the
    data, with Maritz-Jarrett estimators.

    Parameters
    ----------
    data : ndarray
        Data array.
    prob : sequence, optional
        Sequence of quantiles to compute.
    alpha : float, optional
        Confidence level of the intervals.
    axis : int or None, optional
        Axis along which to compute the quantiles.
        If None, use a flattened array.

    Returns
    -------
    ci_lower : ndarray
        The lower boundaries of the confidence interval.  Of the same length as
        `prob`.
    ci_upper : ndarray
        The upper boundaries of the confidence interval.  Of the same length as
        `prob`.

    """
    alpha = min(alpha, 1 - alpha)
    z = norm.ppf(1 - alpha/2.)
    xq = mstats.mquantiles(data, prob, alphap=0, betap=0, axis=axis)
    smj = mjci(data, prob, axis=axis)
    return (xq - z * smj, xq + z * smj) 

# 需要导入模块: from scipy.stats.distributions import norm [as 别名]
# 或者: from scipy.stats.distributions.norm import ppf [as 别名]
def test_null_constrained():

    # Create a mixed population of Z-scores: 1000 standard normal and
    # 20 uniformly distributed between 3 and 4.
    grid = np.linspace(0.001, 0.999, 1000)
    z0 = norm.ppf(grid)
    z1 = np.linspace(3, 4, 20)
    zs = np.concatenate((z0, z1))

    for estimate_mean in False,True:
        for estimate_scale in False,True:
            for estimate_prob in False,True:

                emp_null = NullDistribution(zs, estimate_mean=estimate_mean,
                                            estimate_scale=estimate_scale,
                                            estimate_null_proportion=estimate_prob)

                if not estimate_mean:
                    assert_allclose(emp_null.mean, 0, atol=1e-5, rtol=1e-5)
                if not estimate_scale:
                    assert_allclose(emp_null.sd, 1, atol=1e-5, rtol=1e-2)
                if not estimate_prob:
                    assert_allclose(emp_null.null_proportion, 1, atol=1e-5, rtol=1e-2)

                # consistency check
                assert_allclose(emp_null.pdf(np.r_[-1, 0, 1]),
                                norm.pdf(np.r_[-1, 0, 1], loc=emp_null.mean,
                                         scale=emp_null.sd),
                                rtol=1e-13) 

# 需要导入模块: from scipy.stats.distributions import norm [as 别名]
# 或者: from scipy.stats.distributions.norm import ppf [as 别名]
def mquantiles_cimj(data, prob=[0.25,0.50,0.75], alpha=0.05, axis=None):
    """
    Computes the alpha confidence interval for the selected quantiles of the
    data, with Maritz-Jarrett estimators.

    Parameters
    ----------
    data : ndarray
        Data array.
    prob : sequence
        Sequence of quantiles to compute.
    alpha : float
        Confidence level of the intervals.
    axis : integer
        Axis along which to compute the quantiles.
        If None, use a flattened array.

    """
    alpha = min(alpha, 1-alpha)
    z = norm.ppf(1-alpha/2.)
    xq = mstats.mquantiles(data, prob, alphap=0, betap=0, axis=axis)
    smj = mjci(data, prob, axis=axis)
    return (xq - z * smj, xq + z * smj)


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# 需要导入模块: from scipy.stats.distributions import norm [as 别名]
# 或者: from scipy.stats.distributions.norm import ppf [as 别名]
def trimmed_mean_ci(data, limits=(0.2,0.2), inclusive=(True,True),
                    alpha=0.05, axis=None):
    """
    Selected confidence interval of the trimmed mean along the given axis.

    Parameters
    ----------
    data : array_like
        Input data.
    limits : {None, tuple}, optional
        None or a two item tuple.
        Tuple of the percentages to cut on each side of the array, with respect
        to the number of unmasked data, as floats between 0. and 1. If ``n``
        is the number of unmasked data before trimming, then
        (``n * limits[0]``)th smallest data and (``n * limits[1]``)th
        largest data are masked.  The total number of unmasked data after
        trimming is ``n * (1. - sum(limits))``.
        The value of one limit can be set to None to indicate an open interval.

        Defaults to (0.2, 0.2).
    inclusive : (2,) tuple of boolean, optional
        If relative==False, tuple indicating whether values exactly equal to
        the absolute limits are allowed.
        If relative==True, tuple indicating whether the number of data being
        masked on each side should be rounded (True) or truncated (False).

        Defaults to (True, True).
    alpha : float, optional
        Confidence level of the intervals.

        Defaults to 0.05.
    axis : int, optional
        Axis along which to cut. If None, uses a flattened version of `data`.

        Defaults to None.

    Returns
    -------
    trimmed_mean_ci : (2,) ndarray
        The lower and upper confidence intervals of the trimmed data.

    """
    data = ma.array(data, copy=False)
    trimmed = mstats.trimr(data, limits=limits, inclusive=inclusive, axis=axis)
    tmean = trimmed.mean(axis)
    tstde = mstats.trimmed_stde(data,limits=limits,inclusive=inclusive,axis=axis)
    df = trimmed.count(axis) - 1
    tppf = t.ppf(1-alpha/2.,df)
    return np.array((tmean - tppf*tstde, tmean+tppf*tstde)) 

# 需要导入模块: from scipy.stats.distributions import norm [as 别名]
# 或者: from scipy.stats.distributions.norm import ppf [as 别名]
def trimmed_mean_ci(data, limits=(0.2,0.2), inclusive=(True,True),
                    alpha=0.05, axis=None):
    """
    Selected confidence interval of the trimmed mean along the given axis.

    Parameters
    ----------
    data : array_like
        Input data.
    limits : {None, tuple}, optional
        None or a two item tuple.
        Tuple of the percentages to cut on each side of the array, with respect
        to the number of unmasked data, as floats between 0. and 1. If ``n``
        is the number of unmasked data before trimming, then
        (``n`` * `limits[0]`)th smallest data and (``n`` * `limits[1]`)th
        largest data are masked.  The total number of unmasked data after
        trimming is ``n`` * (1. - sum(`limits`)).
        The value of one limit can be set to None to indicate an open interval.

        Defaults to (0.2, 0.2).
    inclusive : (2,) tuple of boolean, optional
        If relative==False, tuple indicating whether values exactly equal to
        the absolute limits are allowed.
        If relative==True, tuple indicating whether the number of data being
        masked on each side should be rounded (True) or truncated (False).

        Defaults to (True, True).
    alpha : float, optional
        Confidence level of the intervals.

        Defaults to 0.05.
    axis : int, optional
        Axis along which to cut. If None, uses a flattened version of `data`.

        Defaults to None.

    Returns
    -------
    trimmed_mean_ci : (2,) ndarray
        The lower and upper confidence intervals of the trimmed data.

    """
    data = ma.array(data, copy=False)
    trimmed = mstats.trimr(data, limits=limits, inclusive=inclusive, axis=axis)
    tmean = trimmed.mean(axis)
    tstde = mstats.trimmed_stde(data,limits=limits,inclusive=inclusive,axis=axis)
    df = trimmed.count(axis) - 1
    tppf = t.ppf(1-alpha/2.,df)
    return np.array((tmean - tppf*tstde, tmean+tppf*tstde))

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