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A Quadratically Self-Modulated Exponential Distribution for Flexible Lifetime Modeling: Properties, Estimation, Simulation, and Application |
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PP: 1621-1644 |
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doi:10.18576/amis/200611
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Author(s) |
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Mohammed Elgarhy,
Rana H. Khashab,
Mundher A. Khaleel,
Nooruldeen A. Noori,
Ghareeb A. Marei,
Neema M. Elharoun,
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Abstract |
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| This paper presents the Quadratically Self-Modulated Exponential (QSME) distribution, a new two-parameter lifetime model, which extends the classical exponential distribution while retaining its simplicity and the richness of interpretability. The exponential distribution is shown as an exact special case for α = 1 but other values of α generate the range of hazard rate shapes, such as bathtub, increasing, stationary shoulder, and increase-decrease-increase. Also, some mathematical and reliability properties are obtained such as survival, cumulative hazard, quantile, moments, incomplete moments, entropy measures, residual life functions, order statistics, stress-strength reliability, and stochastic ordering. We analyze 8 estimation methods using a Monte Carlo simulation with sample sizes 20, 50, 125, and 250. The results show that percentile matching is the best for small samples and maximum likelihood is the most stable overall for moderate and large samples. An application to 128 bladder cancer remission times illustrates the practical use of the model. Among the models that achieved numerical convergence, QSME attained AIC = 832.5577, BIC = 838.2618, and KS = 0.0805 (p = 0.3774), with the smallest information criteria among the converged competitors. |
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