def test_expon(self):
from scipy.stats import expon
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
mean, var, skew, kurt = expon.stats(moments='mvsk')
x = np.linspace(expon.ppf(0.01), expon.ppf(0.99), 100)
ax.plot(x, expon.pdf(x), 'r-', lw=5, alpha=0.6, label='expon pdf')
rv = expon()
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
vals = expon.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], expon.cdf(vals))
self.assertEqual(str(ax), "AxesSubplot(0.125,0.11;0.775x0.77)")
def main():
fix, ax = plt.subplots(1, 1)
mean, var, skew, kurt = expon.stats(moments='mvsk')
x = exp_dist(0.9) #c=0.9
ax.plot(x, expon.pdf(x), 'r-', lw=5, alpha=0.6, label='expon pdf')
#freeze
rv = expon()
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
#generate random num
r = expon.rvs(size=1000)
# compare
#ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
plt.show()
def get_population_average_estimate(param, shape):
size = 100000
if shape == 'normal' or shape == 'contaminated normal':
mu = 0
elif shape == 'lognormal':
mu = lognorm.stats(param, moments='m')
elif shape == 'contaminated chi-squared':
# mu = chi2.stats(4, 0, param, moments='m')
data = chi2.rvs(4, size=size)
contam_inds = np.random.randint(size, size=int(param * size))
data[contam_inds] *= 10
mu = np.mean(data)
elif shape == 'exponential':
mu = expon.stats(0, param, moments='m')
return mu
'r-', lw=5, alpha=0.6, label='gamma cdf')
ax2.set_title('gamma cdf')
# logistic
b = 0.5
mean, var, skew, kurt = logistic.stats(b, moments = 'mvsk')
x = np.linspace(logistic.ppf(0.01, b),
logistic.ppf(0.99, b), 100)
ax3.plot(x, logistic.pdf(x, b),
'g-', lw=5, alpha=0.6, label='gamma pdf')
ax3.set_title('logistic pdf')
ax4.plot(x, logistic.cdf(x, b),
'g-', lw=5, alpha=0.6, label='gamma cdf')
ax4.set_title('logistic cdf')
# exponential
a = 1.99
mean, var, skew, kurt = expon.stats(a, moments = 'mvsk')
x = np.linspace(expon.ppf(0.01, a),
expon.ppf(0.99, a), 100)
ax5.plot(x, expon.pdf(x, a),
'b-', lw=5, alpha=0.6, label='gamma pdf')
ax5.set_title('exponential pdf')
ax6.plot(x, expon.cdf(x, a),
'b-', lw=5, alpha=0.6, label='gamma cdf')
ax6.set_title('exponential cdf')
plt.tight_layout(pad=0.4, w_pad=0.5, h_pad=1.0)
plt.show()
from scipy.stats import binom, expon
import matplotlib.pyplot as plt
import numpy as np
# 离散型的，二项分布
plt.subplot(311)
n = 100
p = 0.5
mean, var, skew, kurt = binom.stats(n, p, moments='mvsk')
# ppf:累积分布函数的反函数。q=0.01时，ppf就是p(X<x)=0.01时的x值
x = np.arange(binom.ppf(0.01, n, p), binom.ppf(0.99, n, p)) # 离散的
# 分布律
plt.plot(x, binom.pmf(x, n, p), 'o')
# 连续型的，指数分布
plt.subplot(312)
plt.title('概率密度')
lambdax = 1 / 5
loc = 0
scale = 1 / lambdax
means, vars, skews, kurts = expon.stats(loc, scale, moments='mvsk')
xx = np.linspace(expon.ppf(0.01, loc, scale), expon.ppf(0.99, loc, scale), 100)
#概率密度
plt.plot(xx, expon.pdf(xx, loc, scale), label='expon')
plt.subplot(313)
plt.title('分布函数')
plt.plot(xx, 1 - np.exp(-lambdax * xx), '*')
plt.show()
print(xx[-1], 1 - np.exp(-lambdax * x[-1]))
plt.legend(loc='upper left', shadow=True)
plt.show()
# ### Exponential Distribution
# In[7]:
#Exponential Distribution
from scipy.stats import expon
loc, scale = 0, 0.67 # Scale is 1/Lambda
x = np.linspace(expon.ppf(0.01, loc, scale), expon.ppf(0.99, loc, scale),
25) #Percent Point Function (inverse of cdf — percentiles)
print("Mean : ", expon.stats(loc, scale, moments='m'))
print("Variance : ", expon.stats(loc, scale, moments='v'))
print("Prob. Dens. Func. : ", expon.pdf(x, loc, scale))
print("Cum. Density Func.: ", expon.cdf(x, loc, scale))
CDF = expon.cdf(x, loc, scale)
fig = plt.figure(figsize=(20, 10))
plt.subplot(221)
plt.plot(x, expon.pdf(x, loc, scale), 'g', ms=8, label='PDF')
plt.xlabel("Sample Space of Exponential Distribution", fontsize=14)
plt.ylabel("PDF", fontsize=14)
plt.title("Probability Distribution of Exponential(λ=1.5) Distribution",
fontsize=16)
plt.xticks(np.arange(0, 5, 1))
plt.yticks(np.arange(0, 1.7, 0.1))
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 testExponential(betta, size):
values = [lhw.rnexp(betta) for i in range(size)]
mean, var = expon.stats(0, betta, moments='mv')
startWork(values, mean, var, "exponential")
pass
beta_est[k]=np.dot(ganma[:,k],x) / sample_sum_of[k]
print(np.abs(beta_true[k]- beta_est[k]))
total_sample=sum(sample_sum_of)
for k in range(K):
alpha_est[k]=sample_sum_of[k]/total_sample
#print(np.sum(np.abs(alpha_true-alpha_est)),'',np.sum(np.abs(beta_true - beta_est)))
print(' '.join(map(str,np.abs(alpha_true-alpha_est))),' '.join(map(str,np.abs(beta_true - beta_est))))
#reusult
print('#alpha_true=',alpha_true)
print('#alpah_est =',alpha_est)
print('#beta_ture',beta_true)
print('#beta',beta_est)
fig,ax=plt.subplots(1,1)
mean, var, skew ,kurt=expon.stats(moments='mvsk')
X=np.linspace(min(x),max(x),)
for k in range(K):
ax.plot(X,0.5*sample*expon.pdf(X,loc=0,scale=beta_true[k]),'r--',lw=2,label='frozen pdf')
ax.plot(X,0.5*sample*expon.pdf(X,loc=0,scale=beta_est[k]),'b--',lw=2,label='frozen pdf')
num_bin=10
hist,bins=np.histogram(x,bins=num_bin)
width=0.6*(bins[1]-bins[0])
center=(bins[:-1]+bins[1:])/2
ax.hist(x,bins,range=(min(x),max(x)),facecolor='b',alpha=0.4)
plt.show()
aVec = norm.stats(loc=[0, 1, 2], scale=[1, 2, 4], moments="mv")
print('vectorized: ')
print(aVec)
# random numbers from multivariate normal
# does not give Multivariate normal!
print('MULTI?! Does not give multivariate Normal!')
rvs = norm.rvs(loc=np.array([0, 1]), scale=np.array([[1, 0], [0, 1]]))
print(rvs)
print('\n\n')
#############################################################
#############################################################
# In general the standardized distribution for a random variable X is
# obtained through the transformation (X - loc) / scale. The
# default values are loc = 0 and scale = 1.
print('exponential dist')
print(expon.stats())
# for exponential dist scale=1/lambda
print(expon.mean(scale=3))
print('UNIFORM!!!:')
# This distribution is constant between loc and loc + scale.
from scipy.stats import uniform
print(uniform.cdf([0, 1, 2, 34, 5], loc=1, scale=4))
print(np.mean(norm.rvs(5, size=500)))
# shape parameters:
from scipy.stats import gamma
print('GAMMA')
print(gamma(a=1, scale=2).stats(moments="mv"))
print(gamma.stats(a=1, scale=2, moments="mv"))
###################################################
def testExpon(): # {{{
"""
Exponential Distribution (指数分布[又叫负指数分布]: continuous)
连续概率分布,用于表示独立随机事件发生的时间间隔。
比如旅客进入机场的时间间隔,打进客服中心电话的时间间隔,中文维基百科新条目出现的时间间隔等等.
lambda: rate parameter
pdf = lambda * exp(-lambda * x)
E(X) = 1/lambda (如果你平均每个小时接到2次电话，那么你预期等待每一次电话的时间是半个小时.)
"""
# 准备数据: 已知lam, 某件事件单位事件发生的次数(频率)
# X轴: 间隔时间
# Y轴: 某时间点上的密度(可以大于1)
lam = 0.5
theta = 1 / lam
xs = np.linspace(expon.ppf(0.01, scale=theta),
expon.ppf(0.99, scale=theta),
num=1000)
# E(X) = 1/lam 即 (theta), D(X) = 1/(lam**2) 即 (theta**2)
mean, var, skew, kurt = expon.stats(loc=0, scale=theta, moments='mvsk')
print("mean: %.2f, var: %.2f, skew: %.2f, kurt: %.2f" %
(mean, var, skew, kurt))
fig, axs = plt.subplots(2, 2)
# fig.set_figheight(10)
# fig.set_figwidth(14)
# print(fig.get_dpi(), fig.get_figheight(), fig.get_figwidth())
# 显示pdf (使用expon.pdf)
ys = expon.pdf(xs, scale=theta)
axs[0][0].plot(xs, ys, 'bo', markersize=5, label='expon pdf')
axs[0][0].legend()
axs[0][0].set_title('lambda = %.2f' % lam)
axs[0][0].set_xlabel(u"间隔时间")
axs[0][0].set_ylabel(u"概率密度")
# 显示pdf (使用np.exp)
ys = lam * np.exp(-lam * xs)
axs[0][1].plot(xs, ys, 'bo', markersize=5, label='np exp')
axs[0][1].legend()
axs[0][1].set_title('lambda = %.2f' % lam)
# 显示cdf
ys = expon.cdf(xs, scale=theta)
axs[1][0].plot(xs, ys, 'bo', markersize=5, label='expon cdf')
axs[1][0].legend()
axs[1][0].set_title('lambda = %.2f' % lam)
# 随机变量RVS
data = expon.rvs(scale=theta, size=1000)
data = np.around(data, decimals=1)
import sys
sys.path.append("../../thinkstats")
import Pmf
pmf = Pmf.MakePmfFromList(data)
xs, ys = pmf.Render()
# axs[1][1].plot(xs, ys, 'bo', markersize=5, label='rvs pmf')
axs[1][1].scatter(xs, ys, label='rvs pmf')
axs[1][1].legend()
axs[1][1].set_xlabel(u"间隔时间")
axs[1][1].set_ylabel(u"量化后的概率")
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()