# Poisson Distribution

## Poisson Distribution

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.

### Example

Generate a random 1x10 distribution for occurrence 2:

from numpy import random

x = random.poisson(lam=2, size=10)

print(x)
Try it Yourself »

## Visualization of Poisson Distribution

### Example

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()

### Result Try it Yourself »

## Difference Between Normal and Poisson Distribution

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.

### Example

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()

### Result Try it Yourself »

## Difference Between Binomial and Poisson Distribution

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`.

### Example

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()

### Result Try it Yourself »

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