Common types of distributions

Here we are discussing a few very common types of probability distributions.

They are:

Normal Distribution:

Normal distribution is a type of continuous probability distribution where the distribution looks something like below with more data accumulated at the central region & gradually less so towards the tails.

Long Tailed Distribution:

Though the normal distribution is the simplest to understand, most data in real life do not follow normal distribution. 

A long tailed distribution is the kind of distribution with a long narrow portion of a frequency distribution, where relatively extreme values occur at low frequency. It looks something like the below.

Student's t-distribution:

This is a family of distributions resembling normal distributions but with thicker tails. The t-distribution is widely used as a reference basis for the distribution of sample means, differences between two sample means, regression parameters, and more. Students t distribution was figured out at a time when computers were not in use in statistics. Though t distribution is not very important from a data scientist's point of view, an intuitive understanding of it is needed as one may encounter t statistic in outputs of statistical software. The name is so because the founder, Gosset published this paper under a pseudo name called "student". Gosset was a brewer at Guiness Brewery & the company didn't want it's competitors to know that they are applying statistics in brewery. Hence he chose the name.

Binomial Distribution:

Binomial as the names suggest means, two outcomes(Yes/No or 0/1). Binomial distribution shows the frequency distribution of number of successes in X trials. A binomial distribution is important as it helps answer questions like,

If the probability of an ad click converting into a purchase is 0.1 then what should be the probability of 0 sales in 1000 ad clicks?

Here is an awesome read on Binomial Distribution. I encourage readers to go check this link out for a better understanding.

Chi-Square Distribution:

Chi-Square Distribution revolves around the idea of counts of items falling into categories.

Chi-Square statistic is used to test how much of the observed value actually fits a specified distribution( Goodness of fit). In a test, a low chi-square value indicates compliance with the expectation & a high chi-square value means the observed value is different from the expected one(i.e. Null Hypothesis).