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Parameter Estimation in Autoregressive Models with Transmuted Exponential-New Weibull Pareto Error Distribution Using EM Algorithm

Nweze, N.O., Maijamaa, B., Onwuamaeze, Charity Uchenna, Adenomon, M.O.

Abstract

Statistical modelling of lifetime and reliability data often requires flexible probability distributions capable of capturing skewness, kurtosis, and heavy-tailed behaviour. The Transmuted Exponential-New Weibull Pareto (TE-NWP) distribution, a recent generalization of the New Weibull Pareto model via the transmutation technique, offers enhanced flexibility in modelling such data by improving tail behaviour. This study focuses on parameter estimation in autoregressive (AR) models when the error term follows the TE-NWP distribution. The Expectation–Maximization (EM) algorithm was utilized to estimate the model parameters efficiently. Simulation experiments were carried out to assess the performance of the proposed estimators by considering bias, mean square error , and root mean square error for different sample sizes. The findings reveal that the EM-based estimators are stable and reliable, with estimation accuracy improving as the sample size increases. This highlights the ability of the EM algorithm to produce efficient and consistent parameter estimates. In addition, the proposed approach enhances the use of the TE–NWP distribution in time series analysis, offering a flexible and robust alternative for modelling asymmetric and heavy-tailed data when standard normality assumptions are not appropriate.

Keywords

Autoregressive (AR) ProcessEM AlgorithmParameter EstimationSimulation StudyHeavy-Tailed Distribution.

References

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