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)