Statistical Distributions- A Brief Introduction
What is a Probability Distribution?
Distribution is a collection of
probabilities associated with an event and event is an outcome. A probability
distribution is a table or an equation that links each outcome of a statistical
experiment with its probability of occurrence. It is broadly based discrete and
continuous variables.
What is a Binomial Distribution?
Binomial Distribution is used when
trials are independent, fixed and random. It is used where only two outcomes
are present. Probability of success is uniform here. It is used in defective
analysis in industries. It is also known as Bernoulli Process.
The mathematical expression for the
same is given below:
Here mean= np and standard deviation=
sqrt of np(-p).
What is a Poisson Distribution?
Poisson Distribution is a discrete
distribution. The number of trials here is not fixed. The probability of an
event is an interval. It is used in defect analysis. Eg: Number of cars
arriving on a highway, number of pixels in an image.
The mathematical expression for the
same is given below:
Here mean= m and standard deviation=
sqrt of m
What is a Normal Distribution?
It is the most used distribution in the
field of statistics and data analysis. It is also known as a Gaussian
Distribution. It is a continuous distribution and shows a bell curve.
Here mean, median and mode coincides.
The distribution is symmetric about its mean. The tail of the distribution runs
parallel to the X-axis without touching it.
Here 68% of the data lies between 1 std
dev away from the mean, 95% of the data lies between 2 std dev away from
the mean, 99.7% of the data lies between
3 std dev away from the mean.
The mathematical expression for the
same is given below:
The expression is also called as Normal
Probability Density Function. The result is referred to as the central limit
theorem.
To standardize Standard Normal Distribution is used and finally a z score formula was derived given below:
Summary!
This article mainly focused on three
very important types of distributions which are widely used in the field of
data science. All distributions are used in different conditions. Normal
Distribution is the most useful in practical use.
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