Uni-variate and bi-variate Inverted Exponential Teissier distribution in Bayesian and non-Bayesian framework to model...

Area of Science:

• Environmental Statistics
• Probability Distributions
• Time Series Analysis

Background:

• Modeling extreme value data and temporal dependence is crucial in environmental statistics.
• Existing probability distributions may not fully capture complex dependencies.
• Accurate forecasting of environmental variables like rainfall is essential for planning and mitigation.

Purpose of the Study:

• To introduce a new Inverted Exponential Teissier (IET) distribution for modeling extreme value data.
• To develop a bi-variate IET (BIET) distribution to analyze dependency structures between geographical random variables.
• To propose a novel time series forecasting algorithm using the BIET distribution and copula for environmental data.

Main Methods:

• Deduction of statistical properties of the IET distribution.
• Parameter estimation using Bayesian and non-Bayesian frameworks.
• Extension to a bi-variate IET (BIET) distribution for dependency analysis.
• Development of a copula-based time series forecasting algorithm assuming stationarity.
• Validation through extensive simulation studies and application to real-world rainfall data.

Main Results:

• The proposed IET and BIET distributions offer a flexible framework for extreme value modeling and dependency analysis.
• The novel forecasting algorithm demonstrated effectiveness in predicting seasonal rainfall.
• Median regression derived from BIET provided accurate monsoon rainfall estimates using summer rainfall as a covariate.
• The method achieved a low Mean Absolute Percentage Error (MAPE) on the test dataset.

Conclusions:

• The Inverted Exponential Teissier distribution and its bi-variate extension provide valuable tools for environmental statistics.
• The developed time series forecasting method shows potential for accurate environmental data prediction.
• The application to Kerala rainfall data highlights the practical utility of the proposed models in analyzing and forecasting environmental phenomena.