Poisson Distribution vs Normal Distribution
Poisson and Normal distribution come from two different principles. Poisson is one example for Discrete Probability Distribution whereas Normal belongs to Continuous Probability Distribution.
Normal Distribution is generally known as ‘Gaussian Distribution’ and most effectively used to model problems that arises in Natural Sciences and Social Sciences. Many rigorous problems are encountered using this distribution. Most common example would be the ‘Observation Errors’ in a particular experiment. Normal distribution follows a special shape called ‘Bell curve’ that makes life easier for modeling large quantity of variables. In the meantime normal distribution originated from ‘Central Limit Theorem’ under which the large number of random variables are distributed ‘normally’. This distribution has symmetric distribution about its mean. Which means evenly distributed from its x- value of ‘Peak Graph Value’.
pdf: 1/√(2πσ^2 ) e^(〖(x-µ)〗^2/(2σ^2 ))
Above mentioned equation is the Probability Density Function of ‘Normal’ and by enlarge, µ and σ2 refers ‘mean’ and ‘variance’ respectively. The most general case of normal distribution is the ‘Standard Normal Distribution’ where µ=0 and σ2=1. This implies the pdf of non-standard normal distribution describes that, the x-value, where the peak has been right shifted and the width of the bell shape has been multiplied by the factor σ, which is later reformed as ‘Standard Deviation’ or square root of ‘Variance’ (σ^2).
On the other hand Poisson is a perfect example for discrete statistical phenomenon. That comes as the limiting case of binomial distribution – the common distribution among ‘Discrete Probability Variables’. Poisson is expected to be used when a problem arise with details of ‘rate’. More importantly, this distribution is a continuum without a break for an interval of time period with the known occurrence rate. For ‘independent’ events one’s outcome does not affect the next happening will be the best occasion, where Poisson comes into play.
So as a whole one must view that both the distributions are from two entirely different perspectives, which violates the most often similarities among them.