Graduate Seminar

Location:  CL 317 and Livestream

Speaker: Amitabh Halder

PhD Student supervised by Affan Shoukat and Andrei Volodin

Title:  Control Charts for INAR(1) process with discrete transmuted record type exponential distribution and Confidence Intervals on Yule's \(Q\)

Zoom: https://uregina-ca.zoom.us/j/92053635111?pwd=U25NcEp6amlGV1YrRDdnUm5qNlhaUT09

Abstract:

In the first part of our presentation, our study introduces innovative control charts, including cumulative sum and exponentially weighted moving average, seamlessly incorporating them with the newly developed INAR(1) process with discrete transmuted record type exponential distributed innovation to address challenges associated with discrete data and dependencies. In the second part of our presentation, we show that estimates of Yule's \(Q\) and estimates of  \( \log Q\) are asymptotically normal.

In this study, we construct the confidence intervals around \(Q\) and \( \log Q\) for possible combinations of direct and inverse binomial sampling schemes by focusing on the proximity of the confidence coefficients to the stated confidence level. Additionally, we employ the Monte Carlo method to estimate the coverage probability, expected length, and standard deviation of the confidence intervals and the simulation outcomes of those intervals are satisfactory. The proposed confidence intervals may be applied to real-life data in all possible combinations of sampling schemes.