On a new PGDUS transformed model using Inverse Weibull distribution

TL;DR

This work introduces the PGDUS-IW(λ,θ,γ) distribution by applying the PGDUS transformation to a two-parameter Inverse Weibull baseline, enabling flexible lifetime modeling for parallel systems. It derives the distribution’s core functions (CDF, PDF, survival, hazard) and order-statistic properties, and develops ML and MPS estimation procedures, including a closed-form expression for $\hat{\gamma}^{MLE}$. A comprehensive simulation study shows ML generally outperforms MPS in bias and MSE, and a real-data analysis demonstrates superior fit of PGDUS-IW relative to competing PGDUS-3-parameter families using KS/AD/CVM tests and information criteria. The paper also formulates the reliability measures $P(T_2<T_1)$ and its multi-component generalization $R_{c,k}$, with closed-form or computable estimators, facilitating practical reliability assessment for parallel systems.

Abstract

The Power Generalized DUS (PGDUS) Transformation is significant in reliability theory, especially for analyzing parallel systems. From the Generalized Extreme Value distribution, Inverse Weibull model particularly has wide applicability in statistics and reliability theory. In this paper we consider PGDUS transformation of Inverse Weibull distribution. The basic statistical characteristics of the new model are derived, and unknown parameters are estimated using Maximum likelihood and Maximum product of spacings methods. Simulation analysis and the reliability parameter P(T2 < T1) are explored. The effectiveness of the model in fitting a real-world dataset is demonstrated, showing better performance compared to other competing distributions.

Figures (4)

• Figure 1: PDF Plot of PGDUS-IW ($\lambda$, $\theta$, $\gamma$) distribution
• Figure 2: Failure-Rate plot of PGDUS-IW ($\lambda$, $\theta$, $\gamma$) distribution
• Figure 3: Theoretical and Empirical CDFs
• Figure 4: Fitted Densities