Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum-Saunders Autoregressive Moving Average...

Area of Science:

• Environmental Science
• Biostatistics
• Statistical Modeling

Background:

• Environmental agencies seek to link mortality rates with pollutants and temperature.
• Standard regression models often fail due to violated Gaussianity assumptions caused by data asymmetry.
• Existing Birnbaum-Saunders models typically do not account for statistical dependence.

Purpose of the Study:

• To propose a novel time-dependent statistical model for analyzing environmental influences on mortality.
• To develop a dynamic autoregressive moving average model with regressors and a conditional Birnbaum-Saunders distribution (RBSARMAX).
• To assess the performance of the new methodology using Monte Carlo simulations.

Main Methods:

• Development of a time-dependent model based on a reparameterized Birnbaum-Saunders (RBS) asymmetric distribution.
• Formulation of a dynamic autoregressive moving average (ARMA) model incorporating regressors and a conditional RBS distribution (RBSARMAX).
• Assessment of statistical performance via Monte Carlo simulation studies.

Main Results:

• The proposed RBSARMAX methodology demonstrates good statistical performance in simulations.
• Application to real-world sensor data shows the model effectively captures temporal mortality patterns.
• The model provides strong evidence for the relationship between mortality, pollution, and temperature over time.

Conclusions:

• The new ARMA formulation is a robust alternative for modeling temporal data, especially in environmental health.
• The RBSARMAX model successfully addresses asymmetry and time-dependent structures in mortality data.
• This approach enhances the understanding of environmental impacts on public health through advanced statistical analysis.