Volume 35, Issue 1

The extreme value theory (EVT) is used to assess the risk of extreme events caused by natural calamities or untoward circumstances in the social and economic sectors. The theory can be used to study the frequency of rare events and to build up a predictive model so that one can attempt to forecast the frequency of such future extreme events such as a financial collapse and the amount of damage from such a collapse. Even though many statistical techniques have been used to analyze the manner in which the Federal Reserve determines the level of the Federal Fund Rates, no known study has used EVT to analyze and predict the extreme fund rates. In this study, the US Federal Funds Rate, one of the most publicized and important economic indicators in the financial world, from 1954–2019 has been analyzed. The contributions of this study are: (1) to provide an appropriate model for the normalized Federal Funds Rate data; (2) to compare several estimation techniques in estimating parameters for two possible models; (3) to predict the maximum economic return rate from a Federal Funds Rate in the future by using the concept of the return period; and (4) to investigate the bias of estimated parameters applying a simulation study. Simulated data and real financial data are used for the study, and the outcome satisfies the efficiency of its application.

The major problem in analyzing control charts is to work with autocorrelated data. This problem can be solved by fitting a suitable model to the data and using the control chart for the residuals. The problem becomes very important, when the distribution of observation is nonnormal, in addition to being autocorrelated. Much recent research has focused on the development of appropriate statistical process control techniques for the autocorrelated data or nonnormal distribution, but few studies have considered monitoring the process mean of both nonnormal and autocorrelated data. In this paper, a simulation study is conducted to compare the performances of the control chart based on the median absolute deviation method (MAD) with those of existing control charts for the skew normal distribution. Simulation results indicate considerable improvement over existing control charts for nonnormal data can be achieved when the control charts with control limits based on the MAD method are used to monitor the process mean of nonnormal autocorrelated data.

Recently, A. S. Krishnan, S. M. Sunoj and N. U. Nair [Some reliability properties of extropy for residual and past lifetime random variables, J. Korean Stat. Soc. 2020, 10.1007/s42952-019-00023-x] introduced past extropy for measuring uncertainty contained in past lifetime of random variables. In the present study, we focus on the past extropy of k -records. The motivation for considering past extropy of k -records has been discussed in detail. We have also illustrated the merit of considering past extropy of k -records over past extropy of classical records and past extropy of original random sample using two real life data sets. Some important properties of past extropy of k -records are discussed in this work. We have expressed past extropy of k -records using past extropy of k -records arising from uniform distribution. The work proposes a simple estimator for past extropy of k -records as well.

We extend the concept of maximum coefficient of determination Max⁡R2\operatorname{Max}R^{2} caused by repeat runs to ideas about a maximum test statistic F0F_{0} and a minimum p -value Min P for regression