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
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
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
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
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
def get_p(sample_mean, population_mean_null, deviation, length, one=True):
z = get_z_two_queues(sample_mean, population_mean_null, deviation, length)
size = norm(1, 0, 0, z)
if (one):
return 0.5 - size
return (0.5 - size) * 2
def get_z(coefficient):
return norm(1, 0, 0, coefficient / 2)