ABSTRACT
In this paper, the Ridge Regression method is employed to estimate the shape parameter of the Lomax distribution (LD). In addition to that, the approaches of both classical and Bayesian are considered with several loss functions as a squared error (SELF), Linear Exponential (LLF), and Composite Linear Exponential (CLLF). As far as Bayesian estimators are concerned, informative and noninformative priors are used to estimate the shape parameter. To examine the performance of the Ridge Regression method, we compared it with classical estimators which included Maximum Likelihood, Ordinary Least Squares, Uniformly Minimum Variance Unbiased Estimator, and Median Method as well as Bayesian estimators. Monte Carlo simulation compares these estimators with respect to the Mean Square Error criteria (MSE's). The result of the simulation mentioned that the Ridge Regression method is promising and can be used in a real environment. where it revealed better performance the than Ordinary Least Squares method for estimating shape parameter.
Subject(s)
Research Design , Bayes Theorem , Computer Simulation , Least-Squares Analysis , Monte Carlo MethodABSTRACT
The Standardized Precipitation Index (SPI) is a vital component of meteorological drought. Several researchers have been using SPI in their studies to develop new methodologies for drought assessment, monitoring, and forecasting. However, it is challenging for SPI to provide quick and comprehensive information about precipitation deficits and drought probability in a homogenous environment. This study proposes a Regional Intensive Continuous Drought Probability Monitoring System (RICDPMS) for obtaining quick and comprehensive information regarding the drought probability and the temporal evolution of the droughts at the regional level. The RICDPMS is based on Monte Carlo Feature Selection (MCFS), steady-state probabilities, and copulas functions. The MCFS is used for selecting more important stations for the analysis. The main purpose of employing MCFS in certain stations is to minimize the time and resources. The use of MCSF makes RICDPMS efficient for drought monitoring in the selected region. Further, the steady-state probabilities are used to calculate regional precipitation thresholds for selected drought intensities, and bivariate copulas are used for modeling complicated dependence structures as persisting between precipitation at varying time intervals. The RICDPMS is validated on the data collected from six meteorological locations (stations) of the northern area of Pakistan. It is observed that the RICDPMS can monitor the regional drought and provide a better quantitative way to analyze deficits with varying drought intensities in the region. Further, the RICDPMS may be used for drought monitoring and mitigation policies.
