Pareto Distribution

What is Pareto Distribution?

The Pareto Distribution, often referred to as the 80-20 Rule or Pareto Principle, is named after Vilfredo Pareto, an Italian economist and sociologist. This concept is used to describe various phenomena in society, science, and nature.

Back in the early 20th century, Vilfredo Pareto noticed that wealth in Italy was distributed in a very unequal way. He created a mathematical formula to represent this uneven distribution.

The core idea of the 80-20 rule is that a small portion of the causes (20%) leads to the majority of the results (80%). But it's important to note that not all imbalances fit this exact 80-20 ratio. The only true "Pareto distributions" have a specific mathematical shape with a value called α, which is approximately 1.16 (log45).

The distribution is skewed and has long tails that are "slowly fading" (i.e., much of the data is in the seats).

Vilfredo Pareto's observation was that about 80% of the wealth in his country was controlled by only 20% of the population. This idea has been widely adopted in various fields, such as economics, productivity, and demographics. It shows that not everything in life has a balanced input-output relationship.

Later, in the 1940s, a well-known expert on product quality named Dr. Joseph M. Juran broadened the definition of Pareto Distribution.

Juran used quality control for commercial production to use the principle and demonstrate that 20% of production process flaws account for 80% of issues with the majority of products.

History of Pareto Distribution

Early in the 20th century, the 80/20 principle was first used in Italy to describe how wealth was distributed among the populace. For example, Vilfredo Pareto discovered that 20% of the pea pods in his garden produced 80% of the peas planted there, which led him to develop the idea of the Pareto Distribution.

He compared this phenomenon to how wealth was distributed in Italy and discovered that 20% of the people held 80% of the nation's wealth. 

The Italian noted that just a small group of wealthy people, who made up roughly 20 percent of the population, owned 80 percent of the land.

Juran asserts that by concentrating on the 20% defect causes, firms could establish more effective quality control procedures and better use their resources. 

The "Quality Control Handbook," written by Juran in 1951, incorporated his modifications to the theory.

This distribution can describe a variety of scenarios where the ratio of the "small" to the "big" is balanced, not just those involving wealth or income. Some people believe the examples below to be roughly Pareto-distributed:

• In Electric Utility Distribution Reliability (80% of the Customer Minutes Interrupted occur on approximately 20% of the days in a given year).
• 80% of the pollution originates from 20% of all factories.
• 20% of employees are responsible for 80% of the results.
• The standardized price returns on individual stocks.
• Sizes of sand particles
• 20% of a company's products represent 80% of sales.

Pareto Distribution Formula

The Pareto Principle, derived from the Pareto distribution, highlights how not everything is distributed equally. It could be used more broadly even if initially intended to say that 20% of the population possesses 80% of the wealth.

As an illustration, 1% of the populace owns 99% of the wealth. It can simulate any generic circumstance where things are not distributed equally. For instance, 80% of output might be produced by the top 20% of workers.

It has become an indispensable component in the field of research. The log-normal distribution, which uses a random variable whose logarithm is normally distributed, is another frequently used continuous probability distribution. 

A log-normal distribution, based on the accumulation of minor percentage changes, explains various growth processes. 

Particularly in several economics and social sciences phenomena, a log-normally distributed variable replicates a non-negative and non-uniform distribution better than the normal one since it only accepts absolute positive values and is non-symmetric.

The 80/20 principle can be determined using the following formula:

Where:

• x: the random variable
• k: lower bound of the data
• α: the shape parameter

The Pareto Distribution chart can be illustrated as follows:

Practical Applications of the Pareto Distribution

The principle states that in any situation, 20% of the inputs or activities are responsible for 80% of the outputs or the results.

Following are a few of the real-life examples of the Pareto Principle:

1. Farming

a. Vilfredo Pareto observed this law for the first time in his garden. He noticed that 20% of the pea pods generated 80% of the healthy peas. 

b. This observation led him to discover that 80% of the land in Italy was owned by just 20% of the population. We can see this effect in farming, too; 20% of farmland produces 80% of the good crops.

2. Business Operations

a) Business management is one area where the idea of the 80/20 principle is used. For example, a company may see that 20% of the work put into a particular business activity results in 80% of the business results. 

b) This ratio can help a company decide which market sectors are most crucial to concentrate on to maximize efficiency. 

3. Business Revenue

a) 20% of a company's customers produce 80% of the company's revenue. Therefore, when analyzing the source of a company's revenues, the 80-20 rule may also be applicable. 

b) For instance, the business can concentrate on improving the customer satisfaction of influential clients if it notices that 20% of its present customers account for 80% of its reported yearly revenues.

c) The business can further infer from this data that 20% of its customers, who make up most of its transactions, are responsible for 80% of the customer complaints.

d) Additionally, focusing on resolving the grievances of 20% of the company's clients might raise overall client satisfaction. The business should focus on retaining 20% of its influential consumers and gaining new clients.

4. Performance Evaluation

a) The 80-20 rule can be used by a business to assess employee performance. For example, the business may notice that roughly 20% of its employees directly contribute to about 80% of its total output. 

b) Using the ratio, the business can concentrate on paying 20% of the most productive workers to inspire them and push the lower cluster of workers to put in more effort. 

c) The productivity ratio could also demonstrate to the business that 20% of its employees are responsible for 80% of the issues with its human resources.

Pareto Distribution Uses

Our most valuable resource is time, but most don't spend it effectively. While most individuals think that working longer hours will produce better outcomes, there is a difference between being busy and productive.

However, what matters is how you use your time, not how much you put in. You are probably merely busy if you haven't yet used the 80/20 rule in your life. When the idea is applied correctly, it allows you to accomplish more with less effort.

Let's use an example where we declare that 20% of a book will have 80% of the information, which means that 80% of the book will only include 20% of its worth.

Assuming it takes you 20 hours to read the entire book, by applying the principle, you know that 80% of the most critical information could be found in 4 hours. 

If you are a student, this principle will work wonders for you if you notice carefully the exams never contain 100% of the syllabus. Instead, the questions come from 20% of the syllabus, which can help you get an 80%-100% score. 

You will score well if you spend time identifying which 20% of the syllabus is most likely to come for the exam. Studying suitable topics for 4 hours will get you a much better grade than looking for the wrong case for an entire week.

You can also apply this principle to your friendships. For example, you can find that 20% of your friends give you 80% of the joy and fulfillment you get from social interactions.

The other 80% of your friends only give you 20% of the fulfillment. This does not necessarily mean that you have to cut out your friendships with the people that don't bring enough value to your life. Instead, you have to surround yourself more with the ones that do.

It can be applied to almost any area of your life, whether business or free time. If you can identify the 20% that produces the most outcome, you spend more time doing that to create an even greater payout. 

This principle also helps you cut back on 80% of the things that waste your time, which creates only 20% of the value in your life. It encourages you to work efficiently and focus on what is essential.

Therefore, think about the things you should double down on and which ones you should eliminate.

Pareto Distribution and wealth inequality

People that are successful or are excelling in life receive an excessive amount of resources. Statistics show that the poorest 3.5 billion people have the same wealth as the world's top eight richest people.

This wealth gap seems unfair and undoubtedly unequal, affecting not only the amount of money created but also everything else.

The same logic holds for other statistics, such as the number of books published by authors, the population of cities, and the number of trees in a forest.

More problematic than simple capitalism is the inequality issue. It looks like you get inequality as soon as there is a surplus of anything. Among humans, there is inequality in:

• Friendship
• Access to good food
• Healthcare
• Employment, etc. 

Thinking about it purely economically, you start to get inequality as soon as you get a surplus of anything. But unfortunately, it doesn't look like the inequality improvement is within the purview of political organizations. 

The social science on inequality also clearly states that as inequality levels increase, societies tend to destabilize.

Goal setting using the 80/20 principle

Both goal-setting and productivity can be affected by this guideline. For example, 80% of your results will be determined by 20% of your activity, according to this theory. That means if you have a list of 10 things to do, two of them will be more valuable than the other eight things on the list.

The top 10%–most people postpone 20% of the most valued and significant items. People preoccupy themselves with 80% of the least important stuff instead of focusing on the vital few that account for all of their accomplishments.

Have you ever looked back on the school/college projects you've worked on and found that most of your work was done right before the deadline? You could almost say that 80% of your job was done in 20% of your time. 

Start by analyzing and identifying your work process to find out which parts are inefficient and write that down. For example, you might find out that you waste a lot of time in the initial phases of the project by overthinking the problems and procrastinating on the project itself.

Since everything seems so overwhelming, scrolling through social media seems more appealing then. 

Whatever your reasons might be, identify what is inefficient, rearrange your process to avoid them, and implement new strategies like changing their environment to your advantage by removing the options of scrolling through social media. Then, you can get started right away.

Following these steps will help you apply the 80/20 rule to goal-setting and your overall productivity:

1. Write down the top 10 things you need to get done on paper.

2. Then, consider which of those goals would positively influence your life if you were to accomplish just one of them.

3. Pick the second-most important goal, and work toward accomplishing it. After completing this exercise, you'll find that you've determined which 20% of your dreams are most important.

4. Continuously work toward the chosen objectives.

5. Defy the urge to take care of minor issues initially. You will quickly form the habit of beginning again and working on low-value chores if you decide to work on low-value projects first thing in the morning.

For example, 85 percent of the wealthy have a single major objective they are always working toward. On the other hand, only 3% of the impoverished have a significant dream, and they don't work on it frequently. 

Pick one primary objective and devote all your attention to it if you want to be wealthy like wealthy people.

"When your goals are clear, you will come up with exactly the right answers to achieve your goals at exactly the right time" - Brian Tracy.

Researched and authorized by Marazban Tavadia | LinkedIn

Reviewed and edited by Justin Prager-Shulga | LinkedIn

Free Resources 

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