Sometimes, it is hard to connect the mathematical theory that you read at colleges and its real world applications. Things might soon start daunting you if you loose the connection between the two. Although, its not always possible to find application of every thing that you read but if you do find something you must take it pretty seriously to concretize your intuition.
Today, I am going to talk about one of the most famous distribution in probability theory i.e. poisson distribution. It helps to model uncertainity for number of events in a fixed time frame. Now, there is just too much overload of terms. So, let me break down bit by bit for you.
Whenver we talk about probability theory we talk with random experiment. Let’s start with tossing a coin, each time you toss a coin there is always uncertainity involved in it whether it will be head or tail. There is randomness involved in the experiment as you cann’t tell with certainity what will be the precise outcome. In our case tossing a coin will be a random experiment. The set of all possible outcome will be sample space i.e. {Head, Tail}. Any subset of a sample space is defined as an event.
Now, let’s directly dive into the application part. We will take one such example from volcanology. Suppose you have past data of volcanic eruptions i.e. when did it occur and what was its magnitude and you want to predict when will the next eruption occur or what is the probability that more than 1 eruptions will occur in next 100 years. Modelling no of volcanic eruptions can be done using poisson distribution. The probability distribution of poisson process is given by:
where N is the random variable denoting the no of volcanic eruptions happening in a particular time frame. lambda is the expected number of events that occur in a time frame. One of the main goal to find this probability will require estimation of parameter lambda. There are various statistical techniques for estimation of parameter based on the observed data such as Maximum likelihood estimation. For more details refer to the paper in reference section.
Other applications include:
- Number of accidents in a successive years
- Number of suicide in an year
- Number of species that go extinct in 100 years
- Number of customers that come during 10–11 PM.
References:
- Statistical analysis of the frequency of eruptions at Furna: shttp://pages.mtu.edu/~raman/papers2/Jonesetal99JVGR.pdf
