What is the Difference Between Poisson Distribution and Normal Distribution?

The Poisson distribution and the normal distribution are two commonly used probability distributions in statistics, but they have some key differences:

1. Type of Data: Poisson distribution is used for discrete data that can only take on integer values, such as the number of calls received per hour at a call center or the number of customers per day at a restaurant. In contrast, the normal distribution is used for continuous data that can take on any value within a specified range, such as the weight of an animal or the height of a plant.
2. Shape of the Distributions: A normal distribution exhibits a bell-shaped curve, also known as a Gaussian distribution, with a single peak at the mean. On the other hand, the shape of a Poisson distribution depends on its parameter, lambda (λ). As the mean (λ) increases, the asymmetry of the distribution decreases.
3. Parameters: In the Poisson distribution, the mean (λ) and variance (also λ) are equal. In a normal distribution, the mean (µ) and standard deviation (σ) are two separate parameters, and the variance (σ^2) is equal to µ times the standard deviation.
4. Symmetry: A normal distribution is symmetrical around its mean, while a Poisson distribution is asymmetrical (right-skewed) when the mean is small. As the mean of a Poisson distribution increases, the asymmetry decreases.

In summary, the main differences between Poisson and normal distributions are the type of data they represent, the shape of the distributions, their parameters, and the symmetry of the distributions.

Comparative Table: Poisson Distribution vs Normal Distribution

Here is a table summarizing the differences between Poisson distribution and Normal distribution:

The Poisson distribution is used for modeling discrete events with a known average rate, while the Normal distribution is used for continuous data. The shape of the Poisson distribution depends on the value of λ, and it can be skewed if the mean is low, with 0 as the mode. On the other hand, the Normal distribution always exhibits a bell shape and is symmetrical. The Poisson distribution has a range of 0 to ∞, while the Normal distribution can take any value from -∞ to ∞.