Ponnambalam Kumaraswamy (often referred to as Poondi Kumaraswamy) was a leading hydrologist from India. Before his death in 1988, at 57 years old, he was the only one to have received both the Homi Bhabha Fellowship and the Jawaharlal Nehru Fellowship, two of the country’s top research awards. He developed the double bounded probability density function (Kumaraswamy distribution). This distribution is in use in electrical, civil, mechanical, and financial engineering applications. - Wikipedia.org
This month marks P Kumaraswamy’s 80th birth anniversary and this article is a series to honor this great scientist. This first part explores P Kumaraswamy’s early years in Mannargudi, Tamil Nadu and is written by P Kumaraswamy’s son K. Ponnambalam.
K Ponnambalam is currently a Professor of Systems Design Engineering, University of Waterloo, Ontario, Canada.
Even before the gentleman reached the door of his house the little boy knew who it was. The old gentleman was wearing all-white clothes in traditional style, carried an umbrella, a U painted on his forehead, pony tail hair, thick glasses, and a slow walk.
Dei Velu! Go and call your father!
Yes sir, the boy ran inside.
Appa, appa, the teacher is here. He wants you.
Ennada? Did you create trouble at school again? Go! Get that belt!.
Before the boy went inside the house, the teacher shouted.
No Mudaliyarsir! No need for that. I have only good news.
One had to feel superior, or be a friend, to call him Mudaliyarsir - the caste name with ‘sir’ suffix. Most would have called him Subinspectorsir. He was a police man who was respected and feared in that town of Mannargudi. He was known to have eliminated single handed, the most feared thug of that town.
Please sit down SeshadriIyengar.
Dei Velu! Go and get some buttermilk for the teacher.
The teacher was happy to sit down and eagerly waited for his drink. It was a searing hot day and he was tired from walking all the way from the school.
Sir, your son Velu has been promoted to sixth form from third form. He doesn’t have to come to our school but go to the high school. Findlay high school would be a good choice.
Are you kicking him out of your school because you cannot manage him?
No sir, no sir. I showed our headmaster all his work and the headmaster himself tested him with fifth form subjects. He agrees with me that Velu cannot waste one more minute in our school.
Don’t you think he is too little to attend a high school when he is not even nine years old?
He is young yes but he is quite tall and has never lost a fight at school. I have seen kids smaller in size going to high schools. So don’t worry.
The teacher drank what Velu brought and left.
This is the story of Kumaraswamy alias Velu , a well-known engineer-scientist. He died at 57 years old. Many of his works are still in practice and one gaining a wider use today.
We will present one of his works and continue exploring it and his other works in future articles.
We will also bring you stories of why Albert Einstein wrote to him, how, in the toilet, he encouraged Prime Minister Nehru to make a decision to help Tamil Nadu, and bring many other stories from his life.
You may have heard of the bell curve, also called the normal probability density function (PDF) and how it is used, for example, to model grades (marks) in a class. A result of this is to give the average grade, in addition to your own grade, to give you an idea of where you stand in the class. Many know that normal PDF does have strong theoretical basis but, in practice, even for a class of 100 pupils, normal distribution rarely is the best model. Moreover, normal PDF can accept negative random values, which is not possible in many problems.
Kumaraswamy was studying rainfall in tropical regions and decided to formulate a new PDF to fit such random values. It is now called the Kumaraswamy PDF. He could have used the Beta PDF which, may be called the mother of most PDFs, but in those days of little computing facilities, it was difficult to use. He came up with the Kumaraswamy PDF which matches in power the Beta PDF and is much simpler and faster to use. See the figure where we fit the data histogram of grades with both the normal PDF and the Kumaraswamy PDF. The average is 0.76. According to the normal PDF, 50% of students are better than average (in fact, it predicts that for every class!) but, the true value is 57% that the Kumaraswamy PDF predicts well. So you are in a ‘good’ class because a significant majority of students are better than average!
There are many resources to study this distribution and you can start with the Wikipedia. We will also explore it further in forthcoming articles.