almost sure convergence and asymptotic convergence in python
up vote
0
down vote
favorite
I want to plot almost sure convergence and asymptotic convergence. But, I do not have the good result (bad convergence). I don't know where is the problem. It maybe Parzen-Rosenblatt estimator. Is it correctly specified?
from matplotlib.pyplot import *
from math import *
from array import *
import numpy as np
from numpy.random import *
from scipy.misc import *
from scipy.stats import *
from scipy import *
from random import *
#N=1000
n=30
lamb=2
X=lamb*tan(pi*(np.reshape(rand(n,1),n)-0.5)) #loi de Cauchy
x=1
alpha=0.45
def k_gaussien(x):
sigma=1
if(sigma>0):
return((1/(sigma*sqrt(2*pi)))*exp(-(x**2/(2*sigma**2))))
def h(n,alpha):
for i in range(1,n):
return (i**(1-alpha))
def f_PR(x,X,alpha): # Parzen-Rosenblatt estimator
global F;
F = ones((n,1))
h_n = h(n,alpha)
for k in range(2,n):
for i in range(1,k):
F[k] = F[k] + k_gaussien((x-X[i])*i**alpha)
F[k] = F[k] * h_n
return F
# Almost sure convergence f_n(x)--> f(x) ps
figure(figsize=(20,10))
fPR=f_PR(x,X,alpha)
t=linspace(-10,10,n);
plot(cumsum(fPR)/t)
plot(t,0*linspace(1,1,n),lw=3)
plot(t,0*linspace(1,1,n),"r--",lw=3)#with Cauchy density
grid(True)
title("convergence presque sure",fontsize=20,color="blue")
# Convergence in mean N(0,e2f(x))
figure(figsize=(20,10))
x=linspace(1,n,n)
Z= sqrt(h(n,alpha))*(fPR-(1/pi)*(lamb/(lamb**2+x**2))) # sqrt(nh_n)(fn(x)-f(x))
hist(Z,bins=linspace(-10,10,50),normed=True)
title("Theoreme limite centrale",fontsize=20,color="blue")
y=linspace(-10,10,100);
v=(1/pi)*(lamb/(lamb**2+y**2)) # standard deviation (sigma)
plot(y,(1/(sqrt(2*pi)*v))*exp((-y**2)/(2*v**2)),'r',lw=3)# I substitute standard deviation(sigma^2) by cauchy density
title("convergence asymptotique", fontsize=20,color="blue")
python simulation
edited Nov 11 at 17:48
Thierry Lathuille
7,12182630
asked Nov 11 at 17:46
Sa Majesté
83
add a comment |
up vote
0
down vote
favorite
I want to plot almost sure convergence and asymptotic convergence. But, I do not have the good result (bad convergence). I don't know where is the problem. It maybe Parzen-Rosenblatt estimator. Is it correctly specified?
from matplotlib.pyplot import *
from math import *
from array import *
import numpy as np
from numpy.random import *
from scipy.misc import *
from scipy.stats import *
from scipy import *
from random import *
#N=1000
n=30
lamb=2
X=lamb*tan(pi*(np.reshape(rand(n,1),n)-0.5)) #loi de Cauchy
x=1
alpha=0.45
def k_gaussien(x):
sigma=1
if(sigma>0):
return((1/(sigma*sqrt(2*pi)))*exp(-(x**2/(2*sigma**2))))
def h(n,alpha):
for i in range(1,n):
return (i**(1-alpha))
def f_PR(x,X,alpha): # Parzen-Rosenblatt estimator
global F;
F = ones((n,1))
h_n = h(n,alpha)
for k in range(2,n):
for i in range(1,k):
F[k] = F[k] + k_gaussien((x-X[i])*i**alpha)
F[k] = F[k] * h_n
return F
# Almost sure convergence f_n(x)--> f(x) ps
figure(figsize=(20,10))
fPR=f_PR(x,X,alpha)
t=linspace(-10,10,n);
plot(cumsum(fPR)/t)
plot(t,0*linspace(1,1,n),lw=3)
plot(t,0*linspace(1,1,n),"r--",lw=3)#with Cauchy density
grid(True)
title("convergence presque sure",fontsize=20,color="blue")
# Convergence in mean N(0,e2f(x))
figure(figsize=(20,10))
x=linspace(1,n,n)
Z= sqrt(h(n,alpha))*(fPR-(1/pi)*(lamb/(lamb**2+x**2))) # sqrt(nh_n)(fn(x)-f(x))
hist(Z,bins=linspace(-10,10,50),normed=True)
title("Theoreme limite centrale",fontsize=20,color="blue")
y=linspace(-10,10,100);
v=(1/pi)*(lamb/(lamb**2+y**2)) # standard deviation (sigma)
plot(y,(1/(sqrt(2*pi)*v))*exp((-y**2)/(2*v**2)),'r',lw=3)# I substitute standard deviation(sigma^2) by cauchy density
title("convergence asymptotique", fontsize=20,color="blue")
python simulation
edited Nov 11 at 17:48
Thierry Lathuille
7,12182630
asked Nov 11 at 17:46
Sa Majesté
83
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I want to plot almost sure convergence and asymptotic convergence. But, I do not have the good result (bad convergence). I don't know where is the problem. It maybe Parzen-Rosenblatt estimator. Is it correctly specified?
from matplotlib.pyplot import *
from math import *
from array import *
import numpy as np
from numpy.random import *
from scipy.misc import *
from scipy.stats import *
from scipy import *
from random import *
#N=1000
n=30
lamb=2
X=lamb*tan(pi*(np.reshape(rand(n,1),n)-0.5)) #loi de Cauchy
x=1
alpha=0.45
def k_gaussien(x):
sigma=1
if(sigma>0):
return((1/(sigma*sqrt(2*pi)))*exp(-(x**2/(2*sigma**2))))
def h(n,alpha):
for i in range(1,n):
return (i**(1-alpha))
def f_PR(x,X,alpha): # Parzen-Rosenblatt estimator
global F;
F = ones((n,1))
h_n = h(n,alpha)
for k in range(2,n):
for i in range(1,k):
F[k] = F[k] + k_gaussien((x-X[i])*i**alpha)
F[k] = F[k] * h_n
return F
# Almost sure convergence f_n(x)--> f(x) ps
figure(figsize=(20,10))
fPR=f_PR(x,X,alpha)
t=linspace(-10,10,n);
plot(cumsum(fPR)/t)
plot(t,0*linspace(1,1,n),lw=3)
plot(t,0*linspace(1,1,n),"r--",lw=3)#with Cauchy density
grid(True)
title("convergence presque sure",fontsize=20,color="blue")
# Convergence in mean N(0,e2f(x))
figure(figsize=(20,10))
x=linspace(1,n,n)
Z= sqrt(h(n,alpha))*(fPR-(1/pi)*(lamb/(lamb**2+x**2))) # sqrt(nh_n)(fn(x)-f(x))
hist(Z,bins=linspace(-10,10,50),normed=True)
title("Theoreme limite centrale",fontsize=20,color="blue")
y=linspace(-10,10,100);
v=(1/pi)*(lamb/(lamb**2+y**2)) # standard deviation (sigma)
plot(y,(1/(sqrt(2*pi)*v))*exp((-y**2)/(2*v**2)),'r',lw=3)# I substitute standard deviation(sigma^2) by cauchy density
title("convergence asymptotique", fontsize=20,color="blue")
python simulation
edited Nov 11 at 17:48
Thierry Lathuille
7,12182630
asked Nov 11 at 17:46
Sa Majesté
83
I want to plot almost sure convergence and asymptotic convergence. But, I do not have the good result (bad convergence). I don't know where is the problem. It maybe Parzen-Rosenblatt estimator. Is it correctly specified?
from matplotlib.pyplot import *
from math import *
from array import *
import numpy as np
from numpy.random import *
from scipy.misc import *
from scipy.stats import *
from scipy import *
from random import *
#N=1000
n=30
lamb=2
X=lamb*tan(pi*(np.reshape(rand(n,1),n)-0.5)) #loi de Cauchy
x=1
alpha=0.45
def k_gaussien(x):
sigma=1
if(sigma>0):
return((1/(sigma*sqrt(2*pi)))*exp(-(x**2/(2*sigma**2))))
def h(n,alpha):
for i in range(1,n):
return (i**(1-alpha))
def f_PR(x,X,alpha): # Parzen-Rosenblatt estimator
global F;
F = ones((n,1))
h_n = h(n,alpha)
for k in range(2,n):
for i in range(1,k):
F[k] = F[k] + k_gaussien((x-X[i])*i**alpha)
F[k] = F[k] * h_n
return F
# Almost sure convergence f_n(x)--> f(x) ps
figure(figsize=(20,10))
fPR=f_PR(x,X,alpha)
t=linspace(-10,10,n);
plot(cumsum(fPR)/t)
plot(t,0*linspace(1,1,n),lw=3)
plot(t,0*linspace(1,1,n),"r--",lw=3)#with Cauchy density
grid(True)
title("convergence presque sure",fontsize=20,color="blue")
# Convergence in mean N(0,e2f(x))
figure(figsize=(20,10))
x=linspace(1,n,n)
Z= sqrt(h(n,alpha))*(fPR-(1/pi)*(lamb/(lamb**2+x**2))) # sqrt(nh_n)(fn(x)-f(x))
hist(Z,bins=linspace(-10,10,50),normed=True)
title("Theoreme limite centrale",fontsize=20,color="blue")
y=linspace(-10,10,100);
v=(1/pi)*(lamb/(lamb**2+y**2)) # standard deviation (sigma)
plot(y,(1/(sqrt(2*pi)*v))*exp((-y**2)/(2*v**2)),'r',lw=3)# I substitute standard deviation(sigma^2) by cauchy density
title("convergence asymptotique", fontsize=20,color="blue")
python simulation
python simulation
edited Nov 11 at 17:48
Thierry Lathuille
7,12182630
asked Nov 11 at 17:46
Sa Majesté
83
edited Nov 11 at 17:48
Thierry Lathuille
7,12182630
asked Nov 11 at 17:46
Sa Majesté
83
edited Nov 11 at 17:48
Thierry Lathuille
7,12182630
edited Nov 11 at 17:48
Thierry Lathuille
7,12182630
edited Nov 11 at 17:48
Thierry Lathuille
7,12182630
7,12182630
asked Nov 11 at 17:46
Sa Majesté
83
asked Nov 11 at 17:46
Sa Majesté
83
asked Nov 11 at 17:46
Sa Majesté
83
83
add a comment |
add a comment |
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
StackExchange.using("externalEditor", function () {
StackExchange.using("snippets", function () {
StackExchange.snippets.init();
});
});
}, "code-snippets");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "1"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstackoverflow.com%2fquestions%2f53251479%2falmost-sure-convergence-and-asymptotic-convergence-in-python%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
Thanks for contributing an answer to Stack Overflow!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstackoverflow.com%2fquestions%2f53251479%2falmost-sure-convergence-and-asymptotic-convergence-in-python%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
