The exponential distribution is a probability distribution that is primarily concerned with calculating the time when an event may occur. Typically, exponential distribution follows a pattern under which there are more numbers of small values and only a few large values. One of the most important properties of an exponential distribution is memorylessness, which means that the information that an event has already occurred in the past has no effect on the future probability of the occurrence of the same event. In a nutshell, the exponential distribution is a type of continuous distribution that helps to estimate the time duration when a particular event is likely to happen.
Examples of Exponential Distribution
1. Predict the time when an Earthquake might occur
The exponential distribution is prominently used by seismologists and earth scientists to predict the approximate time when an earthquake is likely to occur in a particular locality. For this purpose, the history of the earthquakes and other natural calamities occurring in a particular locality is recorded and monitored. This data acts as the information and is fed to the exponential distribution function. The output gives an approximate time when the earthquake might occur. This helps the environmental engineers and disaster management officials draft the essential measures to avoid the loss of lives and to minimize the property destruction rate.
2. Call Duration
Let us assume that according to a survey, the average amount of time a person accesses a public telephone for conversation is about fifteen minutes. In such a case, the exponential distribution function can be used to find out the probability that the person standing ahead of you will take less than ten minutes to complete his/her conversation.
3. Change Kept in Pocket/Purse
The change kept in one’s pocket or purse generally follows the exponential distribution. This is because, usually, the number of small currency notes or coins held by a person is more, while the number of large currency notes kept by a person is few.
4. Life Span of Electronic Gadgets
Exponential distribution finds its prime application in calculating the reliability of electronic gadgets such as a laptop, battery, processor, mobile phone, etc. It helps the engineers and manufacturers to know an approximate time after which the product will get ruptured. The engineers use this data to improve the quality of their products by replacing the low-quality components with those having comparatively high quality.
5. Establishing a New Shop
While establishing a new shop, a person tends to consider a variety of factors that may affect his/her business. One of such key factors is the number of customers arriving at the shop during the first week. For this purpose, the entrepreneur makes use of the exponential distribution to roughly estimate the number of customers expected to visit the shop on the inauguration day and on the following days. This helps the shopkeeper keep an appropriate amount of products ready to serve all of his/her customers. The exponential distribution also helps to predict the time duration between the arrival of two consecutive customers.
6. Purchasing Flight Tickets
Most travellers tend to buy their flight or train tickets a few days prior to their actual journey to avoid any last-minute hustle. Assume that maximum customers tend to buy their tickets fifteen days before they actually execute a journey, then the probability that a person will book his/her ticket ten days prior to his actual date of commencing the journey can be calculated with the help of exponential distribution. This helps the flight managers maintain an appropriate customer to occupancy ratio in advance. It also helps the transport marketing managers draft the appropriate deals and offers to attract potential customers and enhance sales.
7. Shoppers at a Shopping Mart
The shoppers at a shopping mart are a prominent example of situations where an exponential distribution is followed. This is because most of the shoppers tend to spend a small amount of money on the products, while only a few of them spend a large amount of money.
8. Time that an Interviewer spends with a candidate
If you are applying for a vacancy and are asked to wait for the interview, you can simply use the exponential distribution to roughly estimate the timing of your interview and predict the time that for how long would it go. For this purpose, the only requirement is that the average time that the interviewer takes to finish the interview of previous candidates is well known.
9. Average Time a Call Centre Employee Spends With the Customer
If the average time that a call centre executive takes to complete his/her given task to communicate with a customer is known to be twenty minutes, then the probability that the executive will handle eight customers per hour can be estimated with the help of exponential distribution. This helps the managers draft an appropriate schedule to tackle all the customers approaching the firm with their concerns. This helps improve the customer satisfaction index.
10. Cars Passing per Minute
If it is known that on average approximately ten cars cross a particular highway every minute, then the probability that seven cars will pass the same highway the following minute can be easily estimated with the help of exponential distribution. It also helps to calculate the time duration between the passing of two consecutive cars, thereby helping the traffic in charge to reduce the traffic problem and to avoid collisions.