The reflected-shifted-truncated Maxwell distribution: properties and applications to reliability analysis
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Abstract
Modeling lifetime and reliability data requires flexible probability distributions capable of capturing diverse hazard rate behaviors and skewness patterns. Classical models often fail to adequately represent left-skewed data with bounded ranges. To address this limitation, the Reflected-Shifted-Truncated Maxwell (RSTM) distribution is introduced as an extension of the classical Maxwell model through reflection, shifting, and truncation. Key statistical properties including moments, hazard rate behavior, and stress–strength reliability are derived. Parameters are estimated using the maximum likelihood method for both complete and right-censored data, and estimator performance is assessed via simulation studies. The effectiveness of the RSTM distribution is illustrated through two fiberglass strength datasets, representative of left-skewed lifetime data. Comparative analysis based on information-theoretic measures demonstrates that the RSTM distribution consistently outperforms competing models, underscoring its potential as a robust tool for modeling leftskewed lifetime and reliability data.
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