def find_optimal_T(bg_rate, m, P):
"""Return T so that m-ph delay from pure BG will be < T with prob. < P.
This is equivalent to find_optimal_T_chi2 but conceptually simpler.
"""
T = erlang.ppf(P, m, scale=1./bg_rate)
return T
def find_optimal_T(bg_rate, m, P):
"""Return T so that m-ph delay from pure BG will be < T with prob. < P.
This is equivalent to find_optimal_T_chi2 but conceptually simpler.
"""
T = erlang.ppf(P, m, scale=1. / bg_rate)
return T
def create_bins(knn_orders,
bins_per_k,
nbar=2.0e-4,
epsilon=5e-3,
upper_stretch=1.25,
lower_stretch=1.25):
bins = np.zeros((len(knn_orders), bins_per_k))
for i in range(bins.shape[0]):
lv = erlang.ppf(epsilon, knn_orders[i]) / nbar
ls = (lv * 3 / (4 * np.pi))**(1. / 3.) / lower_stretch
uv = erlang.ppf(1.0 - epsilon, knn_orders[i]) / nbar
us = (uv * 3 / (4 * np.pi))**(1. / 3.) * upper_stretch
bins[i, :] = np.logspace(np.log10(ls), np.log10(us), bins_per_k)
return bins
def mse():
"""Compute MSE of quantiles from the distributions.
Returns:
(dict): MSEs of `lognorm`, `gamma`, `weibull` and `erlang` in a dict.
"""
# quantiles
quantile_points = [.05,.25,.5,.75,.95]
def _qMSE(q):
return np.mean((q - np.array([2.2,3.8,5.1,6.7,11.5]))**2)
# distributions
distr = continuous()
lognorm_quantiles = lognorm.ppf(quantile_points, *distr['lognorm'])
gamma_quantiles = gamma.ppf(quantile_points, *distr['gamma'])
weibull_quantiles = weibull.ppf(quantile_points, *distr['weibull'])
erlang_quantiles = erlang.ppf(quantile_points, *distr['erlang'])
# MSE
return {
'lognorm': _qMSE(lognorm_quantiles),
'gamma': _qMSE(gamma_quantiles),
'weibull': _qMSE(weibull_quantiles),
'erlang': _qMSE(erlang_quantiles)
}
def main():
parser = argparse.ArgumentParser()
parser.add_argument('-s', '--stages', type=int, required=False,
help='Etapas de la distribución')
parser.add_argument('-l', '--lambdap', type=float, required=True,
nargs='+',
help='Parámetro lambda de cada distribución')
parser.add_argument('-r', '--runs', type=int, required=True,
help='Ejecuciones a realizar por cada simulación')
parser.add_argument('-o', '--output', type=str, required=False,
help='Archivo de salida para la grafica')
parser.add_argument('-d', '--dist', type=str, required=True,
choices=['erlang', 'expon', 'hyperexp'],
help='Distribución a emplear para la simulación')
parser.add_argument('--no-graph', required=False,
help='Suprime la salida como gráfica',
dest='graph', action='store_false')
parser.add_argument('--graph', required=False,
help='Habilita la salida como gráfica (usar con [-o])',
dest='graph', action='store_true')
parser.add_argument('-p', '--probability', required=False, type=float,
help='Probabilidad para la distribución Hiperexp.')
parser.set_defaults(graph=True)
args = parser.parse_args()
# msg = 'Distribución {3} con {0} etapas (lambda={1}) en {2} ejecuciones'
# print msg.format(args.stages, args.lambdap, args.runs, args.dist)
fig, ax = plt.subplots(1, 1)
if args.dist in 'erlang':
if args.stages <= 0:
print 'Error: se necesita un número válido de etapas'
sys.exit(1)
lambdap = args.lambdap[0]
mean, var, skew, kurt = erlang.stats(args.stages, scale=lambdap,
moments='mvsk')
x = np.linspace(erlang.ppf(0.00001, args.stages, scale=lambdap),
erlang.ppf(0.99999, args.stages, scale=lambdap),
num=1000)
rv = erlang(args.stages, scale=lambdap)
ax.plot(x, rv.pdf(x), 'r-', lw=5, alpha=0.6, label='Erlang PDF')
# Generate random numbers with this distribution
r = erlang.rvs(args.stages, scale=lambdap, size=args.runs)
ax.hist(r, bins=20, normed=True, histtype='stepfilled', alpha=0.4,
label='Experimental values')
meanexp = np.mean(r)
varexp = np.var(r)
print 'Mediaexperimental: {0} MediaAnalitica: {1}'.format(meanexp,
mean)
print 'Sigma2_exp: {0} Sigma2_a: {1}'.format(varexp, var)
print 'CoV_exp: {0} CoV_a: {1}'.format(np.sqrt(varexp)/meanexp,
np.sqrt(var)/mean)
elif args.dist in 'expon':
lambdap = args.lambdap[0]
mean, var, skew, kurt = expon.stats(scale=lambdap, moments='mvsk')
x = np.linspace(expon.ppf(0.00001, scale=lambdap),
expon.ppf(0.99999, scale=lambdap),
num=1000)
rv = expon(scale=lambdap)
ax.plot(x, rv.pdf(x), 'r-', lw=5, alpha=0.6, label='Exponential PDF')
# Generate random numbers with this distribution
r = expon.rvs(scale=lambdap, size=args.runs)
ax.hist(r, bins=20, normed=True, histtype='stepfilled', alpha=0.4,
label='Experimental values')
meanexp = np.mean(r)
varexp = np.var(r)
print 'Mediaexperimental: {0} MediaAnalitica: {1}'.format(meanexp,
mean)
print 'Sigma2_exp: {0} Sigma2_a: {1}'.format(varexp, var)
print 'CoV_exp: {0} CoV_a: {1}'.format(np.sqrt(varexp)/meanexp,
np.sqrt(var)/mean)
elif args.dist in 'hyperexp':
rv = hyperexp(args.probability, args.lambdap[0], args.lambdap[1])
x = np.linspace(0.00000001, 10.99999, num=1000)
ax.plot(x, rv.pdf(x), 'r-', lw=5, alpha=0.6, label='HyperExp PDF')
# ax.plot(x, rv.cdf(x), 'b-', lw=2, alpha=0.6, label='HyperExp CDF')
r = rv.rvs(size=args.runs)
ax.hist(r, normed=True, bins=100, range=(0, 11),
histtype='stepfilled', alpha=0.4, label='Experimental values')
meanexp = np.mean(r)
varexp = np.var(r)
mean = rv.mean()
var = rv.standard_dev()**2
print 'Mediaexperimental: {0} MediaAnalitica: {1}'.format(meanexp,
mean)
print 'Sigma2_exp: {0} Sigma2_a: {1}'.format(varexp, var)
print 'CoV_exp: {0} CoV_a: {1}'.format(np.sqrt(varexp)/meanexp,
rv.CoV())
if args.graph:
ax.legend(loc='best', frameon=False)
plt.show()
def main():
parser = argparse.ArgumentParser()
parser.add_argument("-s", "--stages", type=int, required=False, help="Etapas de la distribución")
parser.add_argument(
"-l", "--lambdap", type=float, required=True, nargs="+", help="Parámetro lambda de cada distribución"
)
parser.add_argument("-r", "--runs", type=int, required=True, help="Ejecuciones a realizar por cada simulación")
parser.add_argument("-o", "--output", type=str, required=False, help="Archivo de salida para la grafica")
parser.add_argument(
"-d",
"--dist",
type=str,
required=True,
choices=["erlang", "expon", "hyperexp"],
help="Distribución a emplear para la simulación",
)
parser.add_argument(
"--no-graph", required=False, help="Suprime la salida como gráfica", dest="graph", action="store_false"
)
parser.add_argument(
"--graph",
required=False,
help="Habilita la salida como gráfica (usar con [-o])",
dest="graph",
action="store_true",
)
parser.set_defaults(graph=True)
args = parser.parse_args()
msg = "Distribución {3} con {0} etapas (lambda={1}) en {2} ejecuciones"
print msg.format(args.stages, args.lambdap, args.runs, args.dist)
fig, ax = plt.subplots(1, 1)
if args.dist in "erlang":
if args.stages <= 0:
print "Error: se necesita un número válido de etapas"
sys.exit(1)
lambdap = args.lambdap[0]
mean, var, skew, kurt = erlang.stats(args.stages, scale=lambdap, moments="mvsk")
print "E[X]={0}, var(X)={1}".format(mean, var)
x = np.linspace(
erlang.ppf(0.00001, args.stages, scale=lambdap), erlang.ppf(0.99999, args.stages, scale=lambdap), num=1000
)
rv = erlang(args.stages, scale=lambdap)
ax.plot(x, rv.pdf(x), "r-", lw=5, alpha=0.6, label="Erlang PDF")
# Generate random numbers with this distribution
r = erlang.rvs(args.stages, scale=lambdap, size=args.runs)
ax.hist(r, bins=20, normed=True, histtype="stepfilled", alpha=0.2)
meanexp = np.mean(r)
varexp = np.var(r)
print "Mediaexperimental: {0} MediaAnalitica: {1}".format(meanexp, mean)
print "Sigma2_exp: {0} Sigma2_a: {1}".format(varexp, var)
print "CoV_exp: {0} CoV_a: {1}".format(np.sqrt(varexp) / meanexp, np.sqrt(var) / mean)
elif args.dist in "expon":
lambdap = args.lambdap[0]
mean, var, skew, kurt = expon.stats(scale=lambdap, moments="mvsk")
print "E[X]={0}, var(X)={1}".format(mean, var)
x = np.linspace(expon.ppf(0.00001, scale=lambdap), expon.ppf(0.99999, scale=lambdap), num=1000)
rv = expon(scale=lambdap)
ax.plot(x, rv.pdf(x), "r-", lw=5, alpha=0.6, label="Exponential PDF")
# Generate random numbers with this distribution
r = expon.rvs(scale=lambdap, size=args.runs)
ax.hist(r, bins=20, normed=True, histtype="stepfilled", alpha=0.2)
meanexp = np.mean(r)
varexp = np.var(r)
print "Mediaexperimental: {0} MediaAnalitica: {1}".format(meanexp, mean)
print "Sigma2_exp: {0} Sigma2_a: {1}".format(varexp, var)
print "CoV_exp: {0} CoV_a: {1}".format(np.sqrt(varexp) / meanexp, np.sqrt(var) / mean)
elif args.dist in "hyperexp":
print "HyperExponential RV"
rv = hyperexp(0.1, args.lambdap[0], args.lambdap[1])
x = np.linspace(0.00000001, 10.99999, num=1000)
ax.plot(x, rv.pdf(x), "r-", lw=5, alpha=0.6, label="HyperExp PDF")
# ax.plot(x, rv.cdf(x), 'b-', lw=2, alpha=0.6, label='HyperExp CDF')
r = rv.rvs(size=args.runs)
ax.hist(r, normed=True, bins=100, range=(0, 11), histtype="stepfilled", alpha=0.2)
meanexp = np.mean(r)
varexp = np.var(r)
print "Mediaexperimental: {0} MediaAnalitica: {1}".format(meanexp, mean)
print "Sigma2_exp: {0} Sigma2_a: {1}".format(varexp, var)
print "CoV_exp: {0} CoV_a: {1}".format(np.sqrt(varexp) / meanexp, np.sqrt(var) / mean)
if args.graph:
plt.show()
