Пример #1
0
def mvsdist(data):
    """Return 'frozen' distributions for mean, variance, and standard deviation of data.
    
    Parameters
    ----------
    data : array-like (raveled to 1-d)
    
    Returns
    -------
    mdist : "frozen" distribution object
        Distribution object representing the mean of the data
    vdist : "frozen" distribution object
        Distribution object representing the variance of the data
    sdist : "frozen" distribution object
        Distribution object representing the standard deviation of the data
    """
    x = ravel(data)
    n = len(x)
    if (n < 2):
        raise ValueError, "Need at least 2 data-points."
    xbar = x.mean()
    C = x.var()
    if (n > 1000): # gaussian approximations for large n
        mdist = distributions.norm(loc=xbar, scale=math.sqrt(C/n))
        sdist = distributions.norm(loc=math.sqrt(C), scale=math.sqrt(C/(2.*n)))
        vdist = distributions.norm(loc=C, scale=math.sqrt(2.0/n)*C)
    else:
        nm1 = n-1
        fac = n*C/2.
        val = nm1/2.
        mdist = distributions.t(nm1,loc=xbar,scale=math.sqrt(C/nm1))
        sdist = distributions.gengamma(val,-2,scale=math.sqrt(fac))
        vdist = distributions.invgamma(val,scale=fac)
    return mdist, vdist, sdist
Пример #2
0
def mvsdist(data):
    """Return 'frozen' distributions for mean, variance, and standard deviation of data.

    Parameters
    ----------
    data : array-like (raveled to 1-d)

    Returns
    -------
    mdist : "frozen" distribution object
        Distribution object representing the mean of the data
    vdist : "frozen" distribution object
        Distribution object representing the variance of the data
    sdist : "frozen" distribution object
        Distribution object representing the standard deviation of the data
    """
    x = ravel(data)
    n = len(x)
    if (n < 2):
        raise ValueError("Need at least 2 data-points.")
    xbar = x.mean()
    C = x.var()
    if (n > 1000): # gaussian approximations for large n
        mdist = distributions.norm(loc=xbar, scale=math.sqrt(C/n))
        sdist = distributions.norm(loc=math.sqrt(C), scale=math.sqrt(C/(2.*n)))
        vdist = distributions.norm(loc=C, scale=math.sqrt(2.0/n)*C)
    else:
        nm1 = n-1
        fac = n*C/2.
        val = nm1/2.
        mdist = distributions.t(nm1,loc=xbar,scale=math.sqrt(C/nm1))
        sdist = distributions.gengamma(val,-2,scale=math.sqrt(fac))
        vdist = distributions.invgamma(val,scale=fac)
    return mdist, vdist, sdist
Пример #3
0
def mvsdist(data):
    """'frozen' distributions for mean, variance, and standard deviation of data.

    Parameters
    ----------
    data : array-like
       Converted to 1-d using ravel.  Requires 2 or more data-points

    Returns
    -------
    mdist : "frozen" distribution object
        Distribution object representing the mean of the data
    vdist : "frozen" distribution object
        Distribution object representing the variance of the data
    sdist : "frozen" distribution object
        Distribution object representing the standard deviation of the data

    Notes
    -----
    The return values from bayes_mvs(data) is equivalent to
    tuple((x.mean(), x.interval(0.90)) for x in mvsdist(data))
    
    In other words, calling <dist>.mean() and <dist>.interval(0.90) on the 
    three distribution objects returned from this function will give the same 
    results that are returned from bayes_mvs    
    """
    x = ravel(data)
    n = len(x)
    if (n < 2):
        raise ValueError("Need at least 2 data-points.")
    xbar = x.mean()
    C = x.var()
    if (n > 1000):  # gaussian approximations for large n
        mdist = distributions.norm(loc=xbar, scale=math.sqrt(C / n))
        sdist = distributions.norm(loc=math.sqrt(C),
                                   scale=math.sqrt(C / (2. * n)))
        vdist = distributions.norm(loc=C, scale=math.sqrt(2.0 / n) * C)
    else:
        nm1 = n - 1
        fac = n * C / 2.
        val = nm1 / 2.
        mdist = distributions.t(nm1, loc=xbar, scale=math.sqrt(C / nm1))
        sdist = distributions.gengamma(val, -2, scale=math.sqrt(fac))
        vdist = distributions.invgamma(val, scale=fac)
    return mdist, vdist, sdist
Пример #4
0
def mvsdist(data):
    """'frozen' distributions for mean, variance, and standard deviation of data.

    Parameters
    ----------
    data : array-like
       Converted to 1-d using ravel.  Requires 2 or more data-points

    Returns
    -------
    mdist : "frozen" distribution object
        Distribution object representing the mean of the data
    vdist : "frozen" distribution object
        Distribution object representing the variance of the data
    sdist : "frozen" distribution object
        Distribution object representing the standard deviation of the data

    Notes
    -----
    The return values from bayes_mvs(data) is equivalent to
    tuple((x.mean(), x.interval(0.90)) for x in mvsdist(data))
    
    In other words, calling <dist>.mean() and <dist>.interval(0.90) on the 
    three distribution objects returned from this function will give the same 
    results that are returned from bayes_mvs    
    """
    x = ravel(data)
    n = len(x)
    if (n < 2):
        raise ValueError("Need at least 2 data-points.")
    xbar = x.mean()
    C = x.var()
    if (n > 1000): # gaussian approximations for large n
        mdist = distributions.norm(loc=xbar, scale=math.sqrt(C/n))
        sdist = distributions.norm(loc=math.sqrt(C), scale=math.sqrt(C/(2.*n)))
        vdist = distributions.norm(loc=C, scale=math.sqrt(2.0/n)*C)
    else:
        nm1 = n-1
        fac = n*C/2.
        val = nm1/2.
        mdist = distributions.t(nm1,loc=xbar,scale=math.sqrt(C/nm1))
        sdist = distributions.gengamma(val,-2,scale=math.sqrt(fac))
        vdist = distributions.invgamma(val,scale=fac)
    return mdist, vdist, sdist
Пример #5
0
def mvsdist(data):
    """
    'Frozen' distributions for mean, variance, and standard deviation of data.

    Parameters
    ----------
    data : array_like
        Input array. Converted to 1-D using ravel.
        Requires 2 or more data-points.

    Returns
    -------
    mdist : "frozen" distribution object
        Distribution object representing the mean of the data
    vdist : "frozen" distribution object
        Distribution object representing the variance of the data
    sdist : "frozen" distribution object
        Distribution object representing the standard deviation of the data

    Notes
    -----
    The return values from bayes_mvs(data) is equivalent to
    ``tuple((x.mean(), x.interval(0.90)) for x in mvsdist(data))``.

    In other words, calling ``<dist>.mean()`` and ``<dist>.interval(0.90)``
    on the three distribution objects returned from this function will give
    the same results that are returned from `bayes_mvs`.

    Examples
    --------
    >>> from scipy.stats import mvsdist
    >>> data = [6, 9, 12, 7, 8, 8, 13]
    >>> mean, var, std = mvsdist(data)

    We now have frozen distribution objects "mean", "var" and "std" that we can
    examine:

    >>> mean.mean()
    9.0
    >>> mean.interval(0.95)
    (6.6120585482655692, 11.387941451734431)
    >>> mean.std()
    1.1952286093343936

    """
    x = ravel(data)
    n = len(x)
    if (n < 2):
        raise ValueError("Need at least 2 data-points.")
    xbar = x.mean()
    C = x.var()
    if (n > 1000): # gaussian approximations for large n
        mdist = distributions.norm(loc=xbar, scale=math.sqrt(C/n))
        sdist = distributions.norm(loc=math.sqrt(C), scale=math.sqrt(C/(2.*n)))
        vdist = distributions.norm(loc=C, scale=math.sqrt(2.0/n)*C)
    else:
        nm1 = n-1
        fac = n*C/2.
        val = nm1/2.
        mdist = distributions.t(nm1,loc=xbar,scale=math.sqrt(C/nm1))
        sdist = distributions.gengamma(val,-2,scale=math.sqrt(fac))
        vdist = distributions.invgamma(val,scale=fac)
    return mdist, vdist, sdist