Mixing
Simulate MLE for Poisson distribution
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According to the theory given $X_i$ ~ $Pois(lambda)$ iid, the maximum likelihood must be equal to $sum_i=1^n X_i/n$ in this case $5.01$
from scipy.stats import poisson
from datascience import *
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plots
plots.style.use('fivethirtyeight')
# Poisson r.v.
Pois = Table().with_column('PDF',np.random.poisson(lam=5,size=10000))
Pois.hist()
#log-likelihood
def l(lam):
logs = make_array()
for k in Pois.column(0):
logs = np.log(poisson.pmf(k=k,mu = lam))
return np.sum(logs)
# lambdas
lams = np.arange(3,7,0.1)
# likelihood
ls = make_array()
for lam in lams:
print(lam)
ls = np.append(ls, np.exp(l(lam)))
plots.plot(lams,ls)
However, according to the plot the MLE is approximately when lambda = 3
python maximum-likelihood poisson-distribution simulation
asked 1 hour ago
Sargis Iskandaryan
1104
add a comment |Â
up vote
1
down vote
favorite
According to the theory given $X_i$ ~ $Pois(lambda)$ iid, the maximum likelihood must be equal to $sum_i=1^n X_i/n$ in this case $5.01$
from scipy.stats import poisson
from datascience import *
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plots
plots.style.use('fivethirtyeight')
# Poisson r.v.
Pois = Table().with_column('PDF',np.random.poisson(lam=5,size=10000))
Pois.hist()
#log-likelihood
def l(lam):
logs = make_array()
for k in Pois.column(0):
logs = np.log(poisson.pmf(k=k,mu = lam))
return np.sum(logs)
# lambdas
lams = np.arange(3,7,0.1)
# likelihood
ls = make_array()
for lam in lams:
print(lam)
ls = np.append(ls, np.exp(l(lam)))
plots.plot(lams,ls)
However, according to the plot the MLE is approximately when lambda = 3
python maximum-likelihood poisson-distribution simulation
asked 1 hour ago
Sargis Iskandaryan
1104
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
According to the theory given $X_i$ ~ $Pois(lambda)$ iid, the maximum likelihood must be equal to $sum_i=1^n X_i/n$ in this case $5.01$
from scipy.stats import poisson
from datascience import *
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plots
plots.style.use('fivethirtyeight')
# Poisson r.v.
Pois = Table().with_column('PDF',np.random.poisson(lam=5,size=10000))
Pois.hist()
#log-likelihood
def l(lam):
logs = make_array()
for k in Pois.column(0):
logs = np.log(poisson.pmf(k=k,mu = lam))
return np.sum(logs)
# lambdas
lams = np.arange(3,7,0.1)
# likelihood
ls = make_array()
for lam in lams:
print(lam)
ls = np.append(ls, np.exp(l(lam)))
plots.plot(lams,ls)
However, according to the plot the MLE is approximately when lambda = 3
python maximum-likelihood poisson-distribution simulation
asked 1 hour ago
Sargis Iskandaryan
1104
According to the theory given $X_i$ ~ $Pois(lambda)$ iid, the maximum likelihood must be equal to $sum_i=1^n X_i/n$ in this case $5.01$
from scipy.stats import poisson
from datascience import *
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plots
plots.style.use('fivethirtyeight')
# Poisson r.v.
Pois = Table().with_column('PDF',np.random.poisson(lam=5,size=10000))
Pois.hist()
#log-likelihood
def l(lam):
logs = make_array()
for k in Pois.column(0):
logs = np.log(poisson.pmf(k=k,mu = lam))
return np.sum(logs)
# lambdas
lams = np.arange(3,7,0.1)
# likelihood
ls = make_array()
for lam in lams:
print(lam)
ls = np.append(ls, np.exp(l(lam)))
plots.plot(lams,ls)
However, according to the plot the MLE is approximately when lambda = 3
python maximum-likelihood poisson-distribution simulation
python maximum-likelihood poisson-distribution simulation
asked 1 hour ago
Sargis Iskandaryan
1104
asked 1 hour ago
Sargis Iskandaryan
1104
asked 1 hour ago
Sargis Iskandaryan
1104
asked 1 hour ago
Sargis Iskandaryan
1104
asked 1 hour ago
Sargis Iskandaryan
1104
1104
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
down vote
accepted
I got this plot, which looks pretty good, $lambda _mle approx5 approx lambda$
answered 25 mins ago
Cherny
38416
Did you use the same code?
– Sargis Iskandaryan
21 mins ago
yap! on python 3.7... though I needed to install the datascience package, never heard of it before. Oh and I remove the Pois.hist(), since it resulted in an error
– Cherny
19 mins ago
Ok, thank you. It is strange because I have been struggling with this two days. The plot I get looks like an exponential decay.
– Sargis Iskandaryan
9 mins ago
BTW datascience package is from berkeley course data8. Here is a link if you are interested data8.org/fa16
– Sargis Iskandaryan
5 mins ago
Not sure about the exponential decay, but maybe you looked at the distribution of the inverse? I don't want to confuse you too much but you can look at the time between events and you'll get exponential distribution, and Thanks! I'll check it out
– Cherny
2 mins ago
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
I got this plot, which looks pretty good, $lambda _mle approx5 approx lambda$
answered 25 mins ago
Cherny
38416
Did you use the same code?
– Sargis Iskandaryan
21 mins ago
yap! on python 3.7... though I needed to install the datascience package, never heard of it before. Oh and I remove the Pois.hist(), since it resulted in an error
– Cherny
19 mins ago
Ok, thank you. It is strange because I have been struggling with this two days. The plot I get looks like an exponential decay.
– Sargis Iskandaryan
9 mins ago
BTW datascience package is from berkeley course data8. Here is a link if you are interested data8.org/fa16
– Sargis Iskandaryan
5 mins ago
Not sure about the exponential decay, but maybe you looked at the distribution of the inverse? I don't want to confuse you too much but you can look at the time between events and you'll get exponential distribution, and Thanks! I'll check it out
– Cherny
2 mins ago
add a comment |Â
up vote
2
down vote
accepted
I got this plot, which looks pretty good, $lambda _mle approx5 approx lambda$
answered 25 mins ago
Cherny
38416
Did you use the same code?
– Sargis Iskandaryan
21 mins ago
yap! on python 3.7... though I needed to install the datascience package, never heard of it before. Oh and I remove the Pois.hist(), since it resulted in an error
– Cherny
19 mins ago
Ok, thank you. It is strange because I have been struggling with this two days. The plot I get looks like an exponential decay.
– Sargis Iskandaryan
9 mins ago
BTW datascience package is from berkeley course data8. Here is a link if you are interested data8.org/fa16
– Sargis Iskandaryan
5 mins ago
Not sure about the exponential decay, but maybe you looked at the distribution of the inverse? I don't want to confuse you too much but you can look at the time between events and you'll get exponential distribution, and Thanks! I'll check it out
– Cherny
2 mins ago
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
I got this plot, which looks pretty good, $lambda _mle approx5 approx lambda$
answered 25 mins ago
Cherny
38416
I got this plot, which looks pretty good, $lambda _mle approx5 approx lambda$
answered 25 mins ago
Cherny
38416
answered 25 mins ago
Cherny
38416
answered 25 mins ago
Cherny
38416
answered 25 mins ago
Cherny
38416
38416
Did you use the same code?
– Sargis Iskandaryan
21 mins ago
yap! on python 3.7... though I needed to install the datascience package, never heard of it before. Oh and I remove the Pois.hist(), since it resulted in an error
– Cherny
19 mins ago
Ok, thank you. It is strange because I have been struggling with this two days. The plot I get looks like an exponential decay.
– Sargis Iskandaryan
9 mins ago
BTW datascience package is from berkeley course data8. Here is a link if you are interested data8.org/fa16
– Sargis Iskandaryan
5 mins ago
Not sure about the exponential decay, but maybe you looked at the distribution of the inverse? I don't want to confuse you too much but you can look at the time between events and you'll get exponential distribution, and Thanks! I'll check it out
– Cherny
2 mins ago
add a comment |Â
Did you use the same code?
– Sargis Iskandaryan
21 mins ago
yap! on python 3.7... though I needed to install the datascience package, never heard of it before. Oh and I remove the Pois.hist(), since it resulted in an error
– Cherny
19 mins ago
Ok, thank you. It is strange because I have been struggling with this two days. The plot I get looks like an exponential decay.
– Sargis Iskandaryan
9 mins ago
BTW datascience package is from berkeley course data8. Here is a link if you are interested data8.org/fa16
– Sargis Iskandaryan
5 mins ago
Not sure about the exponential decay, but maybe you looked at the distribution of the inverse? I don't want to confuse you too much but you can look at the time between events and you'll get exponential distribution, and Thanks! I'll check it out
– Cherny
2 mins ago
Did you use the same code?
– Sargis Iskandaryan
21 mins ago
Did you use the same code?
– Sargis Iskandaryan
21 mins ago
yap! on python 3.7... though I needed to install the datascience package, never heard of it before. Oh and I remove the Pois.hist(), since it resulted in an error
– Cherny
19 mins ago
yap! on python 3.7... though I needed to install the datascience package, never heard of it before. Oh and I remove the Pois.hist(), since it resulted in an error
– Cherny
19 mins ago
Ok, thank you. It is strange because I have been struggling with this two days. The plot I get looks like an exponential decay.
– Sargis Iskandaryan
9 mins ago
Ok, thank you. It is strange because I have been struggling with this two days. The plot I get looks like an exponential decay.
– Sargis Iskandaryan
9 mins ago
BTW datascience package is from berkeley course data8. Here is a link if you are interested data8.org/fa16
– Sargis Iskandaryan
5 mins ago
BTW datascience package is from berkeley course data8. Here is a link if you are interested data8.org/fa16
– Sargis Iskandaryan
5 mins ago
Not sure about the exponential decay, but maybe you looked at the distribution of the inverse? I don't want to confuse you too much but you can look at the time between events and you'll get exponential distribution, and Thanks! I'll check it out
– Cherny
2 mins ago
Not sure about the exponential decay, but maybe you looked at the distribution of the inverse? I don't want to confuse you too much but you can look at the time between events and you'll get exponential distribution, and Thanks! I'll check it out
– Cherny
2 mins ago
add a comment |Â
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