# Types of Probability Distributions Every Data Science Expert Should know

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Data Science has become one of the most popular interdisciplinary fields. It uses scientific approaches, methods, algorithms, and operations to obtain facts and insights from unstructured, semi-structured, and structured datasets. Organizations use these collected facts and insights for efficient production, business growth, and to predict user requirements. Probability distribution plays a significant role in performing data analysis equipping a dataset for training a model. In this article, you will learn about the types of Probability Distribution, random variables, types of discrete distributions, and continuous distribution.

## What is Probability Distribution?

A Probability Distribution is a statistical method that determines all the probable values and possibilities that a random variable can deliver from a particular range. This range of values will have a lower bound and an upper bound, which we call the minimum and the maximum possible values.

Various factors on which plotting of a value depends are standard deviation, mean (or average), skewness, and kurtosis. All of these play a significant role in Data science as well. We can use probability distribution in physics, engineering, finance, data analysis, machine learning, etc.

## Significance of Probability distributions in Data Science

In a way, most of the data science and machine learning operations are dependent on several assumptions about the probability of your data. Probability distribution allows a skilled data analyst to recognize and comprehend patterns from large data sets; that is, otherwise, entirely random variables and values. Thus, it makes probability distribution a toolkit based on which we can summarize a large data set. The density function and distribution techniques can also help in plotting data, thus supporting data analysts to visualize data and extract meaning.

### General Properties of Probability Distributions

Probability distribution determines the likelihood of any outcome. The mathematical expression takes a specific value of x and shows the possibility of a random variable with p(x). Some general properties of the probability distribution are –

1. The total of all probabilities for any possible value becomes equal to 1.
2. In a probability distribution, the possibility of finding any specific value or a range of values must lie between 0 and 1.
3. Probability distributions tell us the dispersal of the values from the random variable. Consequently, the type of variable also helps determine the type of probability distribution.

### Common Data Types

Before jumping directly into explaining the different probability distributions, let us first understand the different types of probability distributions or the main categories of the probability distribution. Data analysts and data engineers have to deal with a broad spectrum of data, such as text, numerical, image, audio, voice, and many more. Each of these have a specific means to be represented and analyzed. Data in a probability distribution can either be discrete or continuous. Numerical data especially takes one of the two forms.

• Discrete data: They take specific values where the outcome of the data remains fixed. Like, for example, the consequence of rolling two dice or the number of overs in a T-20 match. In the first case, the result lies between 2 and 12. In the second case, the event will be less than 20. Different types of discrete distributions that use discrete data are:
• Binomial Distribution
• Hypergeometric Distribution
• Geometric Distribution
• Poisson Distribution
• Negative Binomial Distribution
• Multinomial Distribution
• Continuous data: It can obtain any value irrespective of bound or limit. Example: weight, height, any trigonometric value, age, etc. Different types of continuous distributions that use continuous data are:
• Beta distribution
• Cauchy distribution
• Exponential distribution
• Gamma distribution
• Logistic distribution
• Weibull distribution

## Types of Probability Distribution explained

Here are some of the popular types of Probability distributions used by data science professionals. (Try all the code using Jupyter Notebook)

• Normal Distribution: It is also known as Gaussian distribution. It is one of the simplest types of continuous distribution. This probability distribution is symmetrical around its mean value. It also shows that data at close proximity of the mean is frequently occurring, compared to data that is away from it. Here, mean = 0, variance = finite value

Here, you can see 0 at the center is the Normal Distribution for different mean and variance values.

Here is a code example showing the use of Normal Distribution:

from scipy.stats import norm
import matplotlib.pyplot as mpl
import numpy as np
def normalDist() -> None:
fig, ax = mpl.subplots(1, 1)
mean, var, skew, kurt = norm.stats(moments = 'mvsk')
x = np.linspace(norm.ppf(0.01),  norm.ppf(0.99), 100)
ax.plot(x, norm.pdf(x),
'r-', lw = 5, alpha = 0.6, label = 'norm pdf')
ax.plot(x, norm.cdf(x),
'b-', lw = 5, alpha = 0.6, label = 'norm cdf')
vals = norm.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], norm.cdf(vals))
r = norm.rvs(size = 1000)
ax.hist(r, normed = True, histtype = 'stepfilled', alpha = 0.2)
ax.legend(loc = 'best', frameon = False)
mpl.show()
normalDist()

Output:

• Bernoulli Distribution: It is the simplest type of probability distribution. It is a particular case of Binomial distribution, where n=1. It means a binomial distribution takes 'n' number of trials, where n > 1 whereas, the Bernoulli distribution takes only a single trial.

Probability Mass Function of a Bernoulli’s Distribution is:

where p = probability of success and q = probability of failure

Here is a code example showing the use of Bernoulli Distribution:

from scipy.stats import bernoulli
import seaborn as sb

def bernoulliDist():
data_bern = bernoulli.rvs(size=1200, p = 0.7)
ax = sb.distplot(
data_bern,
kde = True,
color = 'g',
hist_kws = {'alpha' : 1},
kde_kws = {'color': 'y', 'lw': 3, 'label': 'KDE'})
ax.set(xlabel = 'Bernouli Values', ylabel = 'Frequency Distribution')
bernoulliDist()

Output:

• Continuous Uniform Distribution: In this type of continuous distribution, all outcomes are equally possible; each variable gets the same probability of hit as a consequence. This symmetric probabilistic distribution has random variables at an equal interval, with the probability of 1/(b-a).

Here is a code example showing the use of Uniform Distribution:

from numpy import random
import matplotlib.pyplot as mpl
import seaborn as sb
def uniformDist():
sb.distplot(random.uniform(size = 1200), hist = True)
mpl.show()

uniformDist()

Output:

• Log-Normal Distribution: A Log-Normal distribution is another type of continuous distribution of logarithmic values that form a normal distribution. We can transform a log-normal distribution into a normal distribution.

Here is a code example showing the use of Log-Normal Distribution

import matplotlib.pyplot as mpl
def lognormalDist():
muu, sig = 3, 1
s = np.random.lognormal(muu, sig, 1000)
cnt, bins, ignored = mpl.hist(s, 80, normed = True, align ='mid', color = 'y')
x = np.linspace(min(bins), max(bins), 10000)
calc = (np.exp( -(np.log(x) - muu) **2 / (2 * sig**2))
/ (x * sig * np.sqrt(2 * np.pi)))
mpl.plot(x, calc, linewidth = 2.5, color = 'g')
mpl.axis('tight')
mpl.show()
lognormalDist()

Output:

• Pareto Distribution: It is one of the most critical types of continuous distribution. The Pareto Distribution is a skewed statistical distribution that uses power-law to describe quality control, scientific, social, geophysical, actuarial, and many other types of observable phenomena. The distribution shows slow or heavy-decaying tails in the plot, where much of the data reside at its extreme end.

Here is a code example showing the use of Pareto Distribution –

import numpy as np
from matplotlib import pyplot as plt
from scipy.stats import pareto
def paretoDist():
xm = 1.5
alp = [2, 4, 6]
x = np.linspace(0, 4, 800)
output = np.array([pareto.pdf(x, scale = xm, b = a) for a in alp])
plt.plot(x, output.T)
plt.show()
paretoDist()

Output:

• Exponential Distribution: It is a type of continuous distribution that determines the time elapsed between events (in a Poisson process). Let’s suppose, that you have the Poisson distribution model that holds the number of events happening in a given period. We can model the time between each birth using an exponential distribution.

Here is a code example showing the use of Pareto Distribution –

from numpy import random
import matplotlib.pyplot as mpl
import seaborn as sb
def expDist():
sb.distplot(random.exponential(size = 1200), hist = True)
mpl.show()
expDist()

Output:

## Types of the Discrete probability distribution –

There are various types of Discrete Probability Distribution a Data science aspirant should know about. Some of them are –

• Binomial Distribution: It is one of the popular discrete distributions that determine the probability of x success in the 'n' trial. We can use Binomial distribution in situations where we want to extract the probability of SUCCESS or FAILURE from an experiment or survey which went through multiple repetitions. A Binomial distribution holds a fixed number of trials. Also, a binomial event should be independent, and the probability of obtaining failure or success should remain the same.

Here is a code example showing the use of Binomial Distribution –

from numpy import random
import matplotlib.pyplot as mpl
import seaborn as sb

def binomialDist():
sb.distplot(random.normal(loc = 50, scale = 6, size = 1200), hist = False, label = 'normal')
sb.distplot(random.binomial(n = 100, p = 0.6, size = 1200), hist = False, label = 'binomial')
plt.show()

binomialDist()

Output:

• Geometric Distribution: The geometric probability distribution is one of the crucial types of continuous distributions that determine the probability of any event having likelihood ‘p’ andwill happen (occur) after 'n' number of Bernoulli trials. Here 'n' is a discrete random variable. In this distribution, the experiment goes on until we encounter either a success or a failure. The experiment does not depend on the number of trials.

Here is a code example showing the use of Geometric Distribution –

import matplotlib.pyplot as mpl
def probability_to_occur_at(attempt, probability):
return (1-p)**(attempt - 1) * probability
p = 0.3
attempt = 4
attempts_to_show = range(21)[1:]
print('Possibility that this event will occur on the 7th try: ', probability_to_occur_at(attempt, p))
mpl.xlabel('Number of Trials')
mpl.ylabel('Probability of the Event')
barlist = mpl.bar(attempts_to_show, height=[probability_to_occur_at(x, p) for x in attempts_to_show], tick_label=attempts_to_show)
barlist[attempt].set_color('g')
mpl.show()

Output:

• Poisson Distribution: Poisson distribution is one of the popular types of discrete distribution that shows how many times an event has the possibility of occurrence in a specific set of time. We can obtain this by limiting the Bernoulli distribution from 0 to infinity. Data analysts often use the Poisson distributions to comprehend independent events occurring at a steady rate in a given time interval.

Here is a code example showing the use of Poisson Distribution

from scipy.stats import poisson
import seaborn as sb
import numpy as np
import matplotlib.pyplot as mpl
def poissonDist():
mpl.figure(figsize = (10, 10))
data_binom = poisson.rvs(mu = 3, size = 5000)
ax = sb.distplot(data_binom, kde=True, color = 'g',
bins=np.arange(data_binom.min(), data_binom.max() + 1),
kde_kws={'color': 'y', 'lw': 4, 'label': 'KDE'})
ax.set(xlabel = 'Poisson Distribution', ylabel='Data Frequency')
mpl.show()
poissonDist()

Output:

• Multinomial Distribution: A multinomial distribution is another popular type of discrete probability distribution that calculates the outcome of an event having two or more variables. The term multi means more than one. The Binomial distribution is a particular type of multinomial distribution with two possible outcomes - true/false or heads/tails.

Here is a code example showing the use of Multinomial Distribution –

import numpy as np
import matplotlib.pyplot as mpl
np.random.seed(99)
n = 12
pvalue = [0.3, 0.46, 0.22]
s = []
p = []
for size in np.logspace(2, 3):
outcomes = np.random.multinomial(n, pvalue, size=int(size))

prob = sum((outcomes[:,0] == 7) & (outcomes[:,1] == 2) & (outcomes[:,2] == 3))/len(outcomes)
p.append(prob)
s.append(int(size))
fig1 = mpl.figure()
mpl.plot(s, p, 'o-')
mpl.plot(s, [0.0248]*len(s), '--r')
mpl.grid()
mpl.xlim(xmin = 0)
mpl.xlabel('Number of Events')
mpl.ylabel('Function p(X = K)')

Output:

• Negative Binomial Distribution: It is also a type of discrete probability distribution for random variables having negative binomial events. It is also known as the Pascal distribution, where the random variable tells us the number of repeated trials produced during a specific number of experiments.

Here is a code example showing the use of Negative Binomial Distribution –

import matplotlib.pyplot as mpl
import numpy as np
from scipy.stats import nbinom

x = np.linspace(0, 6, 70)
gr, kr = 0.3, 0.7
g = nbinom.ppf(x, gr, kr)
s = nbinom.pmf(x, gr, kr)
mpl.plot(x, g, "*", x, s, "r--")

Output:

Apart from these mentioned distribution types, various other types of probability distributions exist that data science professionals can use to extract reliable datasets. In the next topic, we will understand some interconnections & relationships between various types of probability distributions.

## Relationship between various Probability distributions –

It is surprising to see that different types of probability distributions are interconnected. In the chart shown below, the dashed line is for limited connections between two families of distribution, whereas the solid lines show the exact relationship between them in terms of transformation, variable, type, etc.

Conclusion

Probability distributions are prevalent among data analysts and data science professionals because of their wide usage. Today, companies and enterprises hire data science professionals in many sectors, namely, computer science, health, insurance, engineering, and even social science, where probability distributions appear as fundamental tools for application. It is essential for Data analysts and data scientists. to know the core of statistics. Probability Distributions perform a requisite role in analyzing data and cooking a dataset to train the algorithms efficiently. If you want to learn more about data science - particularly probability distributions and their uses, check out KnowledgeHut's comprehensive Data science course.

### Gaurav Kr. Roy

Author

Mr. Gaurav is a cybersecurity engineer, developer, researcher, and Book-Author who did his B.S.-Cybersecurity from EC-Council University & Masters from LPU. He is an India Book of Record holder, Guest speaker with 7+ years of experience in IT.

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On an average, Machine Learning engineers get higher salaries, than other software developers.Years of experience in the Machine Learning domain, helps you break into data scientist roles, which is not just among the hottest careers of our generation but also a highly respected and lucrative career. Right skills in the right business domain helps you progress and make a mark for yourself in your organization. For example, if you have expertise in pharmaceutical industries and experience working in Machine learning, then you may land job roles as a data scientist consultant in big pharmaceutical companies.Statistics on Machine learning growth and the industries that use MLAccording to a research paper in AI Multiple (https://research.aimultiple.com/ml-stats/), the Machine Learning market will grow to 9 Billion USD by the end of 2022. There are various areas where Machine Learning models and solutions are getting deployed, and businesses see an overall increase of 44% investments in this area. North America is one of the leading regions in the adoption of Machine Learning followed by Asia.The Global Machine Learning market will grow by 42% which is evident from the following graph. Image sourceThere is a huge demand for Machine Learning modelling because of the large use of Cloud Based Applications and Services. The pandemic has changed the face of businesses, making them heavily dependent on Cloud and AI based services. Google, IBM, and Amazon are just some of the companies that have invested heavily in AI and Machine Learning based application development, to provide robust solutions for problems faced by small to large scale businesses. Machine Learning and Cloud based solutions are scalable and secure for all types of business.ML analyses and interprets data patterns, computing and developing algorithms for various business purposes.Advantages of Machine Learning courseNow that we have established the advantages of perusing a career in Machine Learning, let’s understand from where to start our machine learning journey. The best option would be to start with a Machine Learning course. There are various platforms which offer popular Machine Learning courses. One can always start with an online course which is both effective and safe in these COVID times.These courses start with an introduction to Machine Learning and then slowly help you to build your skills in the domain. Many courses even start with the basics of programming languages such as Python, which are important for building Machine Learning models. Courses from reputed institutions will hand hold you through the basics. Once the basics are clear, you may switch to an offline course and get the required certification.Online certifications have the same value as offline classes. They are a great way to clear your doubts and get personalized help to grow your knowledge. These courses can be completed along with your normal job or education, as most are self-paced and can be taken at a time of your convenience. There are plenty of online blogs and articles to aid you in completion of your certification.Machine Learning courses include many real time case studies which help you in understanding the basics and application aspects. Learning and applying are both important and are covered in good Machine Learning Courses. So, do your research and pick an online tutorial that is from a reputable institute.What Does the Career Path in Machine Learning Look Like?One can start their career in Machine Learning domain as a developer or application programmer. But the acquisition of the right skills and experience can lead you to various career paths. Following are some of the career options in Machine Learning (not an exhaustive list):Data ScientistA data scientist is a person with rich experience in a particular business field. A person who has a knowledge of domain, as well as machine learning modelling, is a data scientist. Data Scientists’ job is to study the data carefully and suggest accurate models to improve the business.AI and Machine Learning EngineerAn AI engineer is responsible for choosing the proper Machine Learning Algorithm based on natural language processing and neural network. They are responsible for applying it in AI applications like personalized advertising.  A Machine Learning Engineer is responsible for creating the appropriate models for improvement of the businessData EngineerA Data Engineer, as the name suggests, is responsible to collect data and make it ready for the application of Machine Learning models. Identification of the right data and making it ready for extraction of further insights is the main work of a data engineer.Business AnalystA person who studies the business and analyzes the data to get insights from it is a Business Analyst. He or she is responsible for extracting the insights from the data at hand.Business Intelligence (BI) DeveloperA BI developer uses Machine Learning and Data Analytics techniques to work on a large amount of data. Proper representation of data to suit business decisions, using the latest tools for creation of intuitive dashboards is the role of a BI developer.  Human Machine Interface learning engineerCreating tools using machine learning techniques to ease the human machine interaction or automate decisions, is the role of a Human Machine Interface learning engineer. This person helps in generating choices for users to ease their work.Natural Language Processing (NLP) engineer or developerAs the name suggests, this person develops various techniques to process Natural Language constructs. Building applications or systems using machine learning techniques to build Natural Language based applications is their main task. They create multilingual Chatbots for use in websites and other applications.Why are Machine Learning Roles so popular?As mentioned above, the market growth of AI and ML has increased tremendously over the past years. The Machine Learning Techniques are applied in every domain including marketing, sales, product recommendations, brand retention, creating advertising, understanding the sentiments of customer, security, banking and more. Machine learning algorithms are also used in emails to ease the users work. This says a lot, and proves that a career in Machine Learning is in high demand as all businesses are incorporating various machine learning techniques and are improving their business.One can harness this popularity by skilling up with Machine Learning skills. Machine Learning models are now being used by every company, irrespective of their size--small or big, to get insights on their data and use these insights to improve the business. As every company wishes to grow faster, they are deploying more machine learning engineers to get their work done on time. Also, the migration of businesses to Cloud services for better security and scalability, has increased their requirement for more Machine Learning algorithms and models to cater to their needs.Introducing the Machine learning techniques and solutions has brought huge returns for businesses.  Machine Learning solution providers like Google, IBM, Microsoft etc. are investing in human resources for development of Machine Learning models and algorithms. The tools developed by them are popularly used by businesses to get early returns. It has been observed that there is significant increase in patents in Machine Learning domains since the past few years, indicating the quantum of work happening in this domain.Machine Learning SkillsLet’s visit a few important skills one must acquire to work in the domain of Machine Learning.Programming languagesKnowledge of programming is very important for a career in Machine Learning. Languages like Python and R are popularly used to develop applications using Machine Learning models and algorithms. Python, being the simplest and most flexible language, is very popular for AI and Machine Learning applications. These languages provide rich support of libraries for implementation of Machine Learning Algorithms. A person who is good in programming can work very efficiently in this domain.Mathematics and StatisticsThe base for Machine Learning is mathematics and statistics. Statistics applied to data help in understanding it in micro detail. Many machine learning models are based on the probability theory and require knowledge of linear algebra, transformations etc. A good understanding of statistics and probability increases the early adoption to Machine Learning domain.Analytical toolsA plethora of analytical tools are available where machine learning models are already implemented and made available for use. Also, these tools are very good for visualization purposes. Tools like IBM Cognos, PowerBI, Tableue etc are important to pursue a career as a  Machine Learning engineer.Machine Learning Algorithms and librariesTo become a master in this domain, one must master the libraries which are provided with various programming languages. The basic understanding of how machine learning algorithms work and are implemented is crucial.Data Modelling for Machine Learning based systemsData lies at the core of any Machine Learning application. So, modelling the data to suit the application of Machine Learning algorithms is an important task. Data modelling experts are the heart of development teams that develop machine learning based systems. SQL based solutions like Oracle, SQL Server, and NoSQL solutions are important for modelling data required for Machine Learning applications. MongoDB, DynamoDB, Riak are some important NOSQL based solutions available to process unstructured data for Machine Learning applications.Other than these skills, there are two other skills that may prove to be beneficial for those planning on a career in the Machine Learning domain:Natural Language processing techniquesFor E-commerce sites, customer feedback is very important and crucial in determining the roadmap of future products. Many customers give reviews for the products that they have used or give suggestions for improvement. These feedbacks and opinions are analyzed to gain more insights about the customers buying habits as well as about the products. This is part of natural language processing using Machine Learning. The likes of Google, Facebook, Twitter are developing machine learning algorithms for Natural Language Processing and are constantly working on improving their solutions. Knowledge of basics of Natural Language Processing techniques and libraries is must in the domain of Machine Learning.Image ProcessingKnowledge of Image and Video processing is very crucial when a solution is required to be developed in the area of security, weather forecasting, crop prediction etc. Machine Learning based solutions are very effective in these domains. Tools like Matlab, Octave, OpenCV are some important tools available to develop Machine Learning based solutions which require image or video processing.ConclusionMachine Learning is a technique to automate the tasks based on past experiences. This is among the most lucrative career choices right now and will continue to remain so in the future. Job opportunities are increasing day by day in this domain. Acquiring the right skills by opting for a proper Machine Learning course is important to grow in this domain. You can have an impressive career trajectory as a machine learning expert, provided you have the right skills and expertise.
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Why Should You Start a Career in Machine Learning?

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