#ResearchatNITR: The Mathematics Edition
Magna Mishra | Jan 13, 2020
Its the subject of numbers, logic, common sense and above all, its the backbone of many engineering disciplines. Today, we take a look at one of the ongoing research projects in the Department of Mathematics. The project in focus is called Stochastic inequalities between extreme order statistics when random samples are independent and interdependent and is headed by Professor Suchandan Kayal. It has been sponsored by SERB(Science and Engineering Research Board) and the duration is from March 2019 to March 2022.
The term "stochastic" is used to describe a process which has random probability distribution or pattern that can be analysed and predicted, but not accurately. The above project under the Department of Mathematics compares the extreme order statistics arising from 2 systems or collections of random variables by estimating the lifetimes of their components. It is assumed that the random variables follow a family of parametric probability models. Systems can be parallel or series. Depending on the type of system, the project evaluates either the maximum likelihood or the minimum. Comparison is done by considering different Stochastic orders such as hazard rate order, likelihood residual order and mean residual order.
Mathematical concepts such as calculus, monotonicity, optimisation were also used in addition to statistics.
The project doesn't require any particular software since it is a theoretical project. However, software such as MATHEMATICA and MATLAB are employed while making graphs.
While speaking about the practical implications of the project, Professor Suchandan Kayal said:
This project has 2 major applications, one- to estimate and compare the lifetimes of 2 engineering systems, which can be parallel or series. Secondly, we can use the results to compare the smallest or largest claim amount arising from heterogeneous insurance portfolios of risk. Besides this, we can use the outputs of the project in auction theory to compare final prices in the sealed-bid first-price auctions.