Poisson Distribution is a Discrete Distribution.
It estimates how many times an event can happen in a specified time. e.g. If someone eats twice a day what is the probability he will eat thrice?
It has two parameters:
lam
- rate or known number of occurrences e.g. 2 for above problem.
size
- The shape of the returned array.
Generate a random 1x10 distribution for occurrence 2:
from numpy import random
x = random.poisson(lam=2, size=10)
print(x)
Try it Yourself »
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns
sns.distplot(random.poisson(lam=2, size=1000), kde=False)
plt.show()
Normal distribution is continuous whereas poisson is discrete.
But we can see that similar to binomial for a large enough poisson distribution it will become similar to normal distribution with certain std dev and mean.
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns
sns.distplot(random.normal(loc=50, scale=7, size=1000), hist=False, label='normal')
sns.distplot(random.poisson(lam=50, size=1000), hist=False, label='poisson')
plt.show()
Binomial distribution only has two possible outcomes, whereas poisson distribution can have unlimited possible outcomes.
But for very large n
and near-zero p
binomial distribution is near identical to poisson distribution such that n * p
is nearly equal to lam
.
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns
sns.distplot(random.binomial(n=1000, p=0.01, size=1000), hist=False, label='binomial')
sns.distplot(random.poisson(lam=10, size=1000), hist=False, label='poisson')
plt.show()
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