def ppcc_plot(x,a,b,dist='tukeylambda', plot=None, N=80):
"""Returns (shape, ppcc), and optionally plots shape vs. ppcc
(probability plot correlation coefficient) as a function of shape
parameter for a one-parameter family of distributions from shape
value a to b.
See also ppcc_max
"""
svals = r_[a:b:complex(N)]
ppcc = svals*0.0
k=0
for sval in svals:
r1,r2 = probplot(x,sval,dist=dist,fit=1)
ppcc[k] = r2[-1]
k += 1
if plot is not None:
try:
import scipy.xplt as xplt
xplt.limits()
except: pass
plot.plot(svals, ppcc, 'x')
plot.title('(%s) PPCC Plot' % dist)
plot.xlabel('Prob Plot Corr. Coef.',deltay=-0.01)
plot.ylabel('Shape Values',deltax=-0.01)
try: plot.expand_limits(5)
except: pass
return svals, ppcc
def probplot(x, sparams=(), dist='norm', fit=1, plot=None):
"""Return (osm, osr){,(scale,loc,r)} where (osm, osr) are order statistic
medians and ordered response data respectively so that plot(osm, osr)
is a probability plot. If fit==1, then do a regression fit and compute the
slope (scale), intercept (loc), and correlation coefficient (r), of the
best straight line through the points. If fit==0, only (osm, osr) is
returned.
sparams is a tuple of shape parameter arguments for the distribution.
"""
N = len(x)
Ui = zeros(N)*1.0
Ui[-1] = 0.5**(1.0/N)
Ui[0] = 1-Ui[-1]
i = arange(2,N)
Ui[1:-1] = (i-0.3175)/(N+0.365)
try:
ppf_func = eval('distributions.%s.ppf'%dist)
except AttributError:
raise dist, "is not a valid distribution with a ppf."
if sparams is None:
sparams = ()
if isscalar(sparams):
sparams = (sparams,)
if not isinstance(sparams,types.TupleType):
sparams = tuple(sparams)
res = inspect.getargspec(ppf_func)
if not ('loc' == res[0][-2] and 'scale' == res[0][-1] and \
0.0==res[-1][-2] and 1.0==res[-1][-1]):
raise ValueError, "Function has does not have default location", \
"and scale parameters\n that are 0.0 and 1.0 respectively."
if (len(sparams) < len(res[0])-len(res[-1])-1) or \
(len(sparams) > len(res[0])-3):
raise ValueError, "Incorrect number of shape parameters."
osm = ppf_func(Ui,*sparams)
osr = sort(x)
if fit or (plot is not None):
# perform a linear fit.
slope, intercept, r, prob, sterrest = stats.linregress(osm,osr)
if plot is not None:
try:
import scipy.xplt as xplt
xplt.limits()
except: pass
plot.plot(osm, osr, 'o', osm, slope*osm + intercept)
plot.title('Probability Plot')
plot.xlabel('Order Statistic Medians')
plot.ylabel('Ordered Values')
try: plot.expand_limits(5)
except: pass
xmin,xmax= amin(osm),amax(osm)
ymin,ymax= amin(x),amax(x)
pos = xmin+0.70*(xmax-xmin), ymin+0.01*(ymax-ymin)
try: plot.addtext("r^2^=%1.4f" % r, xy=pos,tosys=1)
except: pass
if fit:
return (osm, osr), (slope, intercept, r)
else:
return osm, osr
def boxcox_normplot(x,la,lb,plot=None,N=80):
svals = r_[la:lb:complex(N)]
ppcc = svals*0.0
k = 0
for sval in svals:
r1,r2 = probplot(x,dist='norm',fit=1)
ppcc[k] = r2[-1]
k +=1
if plot is not None:
try:
import scipy.xplt as xplt
xplt.limits()
except: pass
plot.plot(svals, ppcc, 'x')
plot.title('Box-Cox Normality Plot')
plot.xlabel('Prob Plot Corr. Coef.',deltay=-0.01)
plot.ylabel('Transformation parameter',deltax=-0.01)
try: plot.expand_limits(5)
except: pass
return svals, ppcc