There are several theorical results about order statistics and copulas in the literature that have  been mentioned also by Nelsen cite{p20}. The present study after reviewing some of these results, relies on  simulation technique to investigate the mentioned results about order statistics and copulas. The study concentrates on two well known Archimedean Gumbel and Frank families in the case tha...

Major advancements have been made in the field of object detection and segmentation recently. However, when it comes to rare categories, state-of-the-art methods fail detect them, resulting a significant performance gap between frequent categories. In this paper, we identify that Sigmoid or Softmax functions used deep detectors are major reason for low sub-optimal long-tailed segmentation. To a...

In this paper, we study the estimation problems for the two-parameter exponentiated Gumbel distribution based on lower record values. An exact confidence interval and an exact joint confidence region for the parameters are constructed. A simulation study is conducted to study the performance of the proposed confidence interval and region. Finally, a numerical example with real data set is gi...