def plot_johnson_sb_fit(data,
fit_results,
title=None,
x_label=None,
x_range=None,
y_range=None,
fig_size=(6, 5),
bin_width=1,
filename=None):
"""
:param data: (numpy.array) observations
:param fit_results: dictionary with keys "a", "b", "loc", "scale", and "AIC"
:param title: title of the figure
:param x_label: label to show on the x-axis of the histogram
:param x_range: (tuple) x range
:param y_range: (tuple) y range
(the histogram shows the probability density so the upper value of y_range should be 1).
:param fig_size: int, specify the figure size
:param bin_width: bin width
:param filename: filename to save the figure as
"""
plot_fit_continuous(data=data,
dist=stat.johnsonsb(a=fit_results['a'],
b=fit_results['b'],
loc=fit_results['loc'],
scale=fit_results['scale']),
label='Johnson Sb',
bin_width=bin_width,
title=title,
x_label=x_label,
x_range=x_range,
y_range=y_range,
fig_size=fig_size,
filename=filename)
def getfracvalsfromfit(histfit, thefracs, numbins=2000, displayplots=True):
"""
Parameters
----------
histfit
thefracs
numbins
displayplots
Returns
-------
"""
# print('entering getfracvalsfromfit: histfit=',histfit, ' thefracs=', thefracs)
thedist = johnsonsb(histfit[0], histfit[1], histfit[2], histfit[3])
# print('froze the distribution')
if displayplots:
themin = 0.001
themax = 0.999
bins = np.arange(themin, themax, (themax - themin) / numbins)
fig = pl.figure()
ax = fig.add_subplot(111)
ax.set_title('probability histogram')
pl.plot(bins, johnsonsb.ppf(thefracs, histfit[0], histfit[1], histfit[2], histfit[3]))
pl.show()
# thevals = johnsonsb.ppf(thefracs, histfit[0], histfit[1], histfit[2], histfit[3])
thevals = thedist.ppf(thefracs)
return thevals
def getjohnsonppf(percentile, params, zeroterm):
"""
Parameters
----------
percentile
params
zeroterm
Returns
-------
"""
johnsonfunc = johnsonsb(params[0], params[1], params[2], params[3])
corrfac = 1.0 - zeroterm
def getjohnsonppf(percentile, params, zeroterm):
"""
Parameters
----------
percentile
params
zeroterm
Returns
-------
"""
johnsonfunc = johnsonsb(params[0], params[1], params[2], params[3])
corrfac = 1.0 - zeroterm
def getfracvalsfromfit(histfit, thefracs):
"""
Parameters
----------
histfit
thefracs
displayplots
Returns
-------
"""
# print('entering getfracvalsfromfit: histfit=',histfit, ' thefracs=', thefracs)
thedist = johnsonsb(histfit[0], histfit[1], histfit[2], histfit[3])
thevals = thedist.ppf(thefracs)
return thevals
def fit_johnsonSb(data, x_label, fixed_location=0, figure_size=5):
"""
:param data: (numpy.array) observations
:param x_label: label to show on the x-axis of the histogram
:param figure_size: int, specify the figure size
:returns: dictionary with keys "a", "b", "loc", "scale", and "AIC"
"""
# plot histogram
fig, ax = plt.subplots(1, 1, figsize=(figure_size + 1, figure_size))
ax.hist(data,
normed=1,
bins='auto',
edgecolor='black',
alpha=0.5,
label='Frequency')
# estimate the parameters
a, b, loc, scale = scs.johnsonsb.fit(data, floc=fixed_location)
# plot the estimated JohnsonSb distribution
x_values = np.linspace(scs.johnsonsb.ppf(0.01, a, b, loc, scale),
scs.johnsonsb.ppf(0.99, a, b, loc, scale), 100)
rv = scs.johnsonsb(a, b, loc, scale)
ax.plot_all(x_values,
rv.pdf(x_values),
color=COLOR_CONTINUOUS_FIT,
lw=2,
label='JohnsonSb')
ax.set_xlabel(x_label)
ax.set_ylabel("Frequency")
ax.legend()
plt.show()
# calculate AIC
aic = AIC(k=3,
log_likelihood=np.sum(
scs.johnsonsb.logpdf(data, a, b, loc, scale)))
# report results in the form of a dictionary
return {"a": a, "b": b, "loc": loc, "scale": scale, "AIC": aic}
def fit_johnson_per_label(X, labels):
'''
Fits a Johnson Distribution (bounded) to a univariate variable X
for each class label in labels
Parameters
----------
X : ndarray, N x T, univariate numeric.
labels : ndarray, integer class labels.
Returns
-------
distributions : list of rv_continous objects.
List of fitted Johnson distributions, indexed by label.
'''
distributions = []
for l in np.unique(labels):
X_l = X[labels == l]
X_lr = X_l.reshape((X_l.shape[0] * X_l.shape[1]), 1)
a, b, loc, scale = stats.johnsonsb.fit(X_lr)
d = stats.johnsonsb(a, b, loc=loc, scale=scale)
distributions.append(d)
return distributions
def all_dists():
# dists param were taken from scipy.stats official
# documentaion examples
# Total - 89
return {
"alpha":
stats.alpha(a=3.57, loc=0.0, scale=1.0),
"anglit":
stats.anglit(loc=0.0, scale=1.0),
"arcsine":
stats.arcsine(loc=0.0, scale=1.0),
"beta":
stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
"betaprime":
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0),
"bradford":
stats.bradford(c=0.299, loc=0.0, scale=1.0),
"burr":
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0),
"cauchy":
stats.cauchy(loc=0.0, scale=1.0),
"chi":
stats.chi(df=78, loc=0.0, scale=1.0),
"chi2":
stats.chi2(df=55, loc=0.0, scale=1.0),
"cosine":
stats.cosine(loc=0.0, scale=1.0),
"dgamma":
stats.dgamma(a=1.1, loc=0.0, scale=1.0),
"dweibull":
stats.dweibull(c=2.07, loc=0.0, scale=1.0),
"erlang":
stats.erlang(a=2, loc=0.0, scale=1.0),
"expon":
stats.expon(loc=0.0, scale=1.0),
"exponnorm":
stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
"exponweib":
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0),
"exponpow":
stats.exponpow(b=2.7, loc=0.0, scale=1.0),
"f":
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0),
"fatiguelife":
stats.fatiguelife(c=29, loc=0.0, scale=1.0),
"fisk":
stats.fisk(c=3.09, loc=0.0, scale=1.0),
"foldcauchy":
stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
"foldnorm":
stats.foldnorm(c=1.95, loc=0.0, scale=1.0),
# "frechet_r": stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
# "frechet_l": stats.frechet_l(c=3.63, loc=0.0, scale=1.0),
"genlogistic":
stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
"genpareto":
stats.genpareto(c=0.1, loc=0.0, scale=1.0),
"gennorm":
stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
"genexpon":
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0),
"genextreme":
stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
"gausshyper":
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0),
"gamma":
stats.gamma(a=1.99, loc=0.0, scale=1.0),
"gengamma":
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0),
"genhalflogistic":
stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
"gilbrat":
stats.gilbrat(loc=0.0, scale=1.0),
"gompertz":
stats.gompertz(c=0.947, loc=0.0, scale=1.0),
"gumbel_r":
stats.gumbel_r(loc=0.0, scale=1.0),
"gumbel_l":
stats.gumbel_l(loc=0.0, scale=1.0),
"halfcauchy":
stats.halfcauchy(loc=0.0, scale=1.0),
"halflogistic":
stats.halflogistic(loc=0.0, scale=1.0),
"halfnorm":
stats.halfnorm(loc=0.0, scale=1.0),
"halfgennorm":
stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
"hypsecant":
stats.hypsecant(loc=0.0, scale=1.0),
"invgamma":
stats.invgamma(a=4.07, loc=0.0, scale=1.0),
"invgauss":
stats.invgauss(mu=0.145, loc=0.0, scale=1.0),
"invweibull":
stats.invweibull(c=10.6, loc=0.0, scale=1.0),
"johnsonsb":
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0),
"johnsonsu":
stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
"ksone":
stats.ksone(n=1e03, loc=0.0, scale=1.0),
"kstwobign":
stats.kstwobign(loc=0.0, scale=1.0),
"laplace":
stats.laplace(loc=0.0, scale=1.0),
"levy":
stats.levy(loc=0.0, scale=1.0),
"levy_l":
stats.levy_l(loc=0.0, scale=1.0),
"levy_stable":
stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
"logistic":
stats.logistic(loc=0.0, scale=1.0),
"loggamma":
stats.loggamma(c=0.414, loc=0.0, scale=1.0),
"loglaplace":
stats.loglaplace(c=3.25, loc=0.0, scale=1.0),
"lognorm":
stats.lognorm(s=0.954, loc=0.0, scale=1.0),
"lomax":
stats.lomax(c=1.88, loc=0.0, scale=1.0),
"maxwell":
stats.maxwell(loc=0.0, scale=1.0),
"mielke":
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0),
"nakagami":
stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
"ncx2":
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0),
"ncf":
stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
"nct":
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0),
"norm":
stats.norm(loc=0.0, scale=1.0),
"pareto":
stats.pareto(b=2.62, loc=0.0, scale=1.0),
"pearson3":
stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
"powerlaw":
stats.powerlaw(a=1.66, loc=0.0, scale=1.0),
"powerlognorm":
stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
"powernorm":
stats.powernorm(c=4.45, loc=0.0, scale=1.0),
"rdist":
stats.rdist(c=0.9, loc=0.0, scale=1.0),
"reciprocal":
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0),
"rayleigh":
stats.rayleigh(loc=0.0, scale=1.0),
"rice":
stats.rice(b=0.775, loc=0.0, scale=1.0),
"recipinvgauss":
stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
"semicircular":
stats.semicircular(loc=0.0, scale=1.0),
"t":
stats.t(df=2.74, loc=0.0, scale=1.0),
"triang":
stats.triang(c=0.158, loc=0.0, scale=1.0),
"truncexpon":
stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
"truncnorm":
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0),
"tukeylambda":
stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
"uniform":
stats.uniform(loc=0.0, scale=1.0),
"vonmises":
stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
"vonmises_line":
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0),
"wald":
stats.wald(loc=0.0, scale=1.0),
"weibull_min":
stats.weibull_min(c=1.79, loc=0.0, scale=1.0),
"weibull_max":
stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
"wrapcauchy":
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0),
}
x = np.linspace(johnsonsb.ppf(0.01, a, b), johnsonsb.ppf(0.99, a, b), 100)
ax.plot(x,
johnsonsb.pdf(x, a, b),
'r-',
lw=5,
alpha=0.6,
label='johnsonsb pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = johnsonsb(a, b)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = johnsonsb.ppf([0.001, 0.5, 0.999], a, b)
np.allclose([0.001, 0.5, 0.999], johnsonsb.cdf(vals, a, b))
# True
# Generate random numbers:
r = johnsonsb.rvs(a, b, size=1000)
# And compare the histogram:
ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
