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Unit ZLindley Distribution with Statistical Properties, Estimation, and Application to Engineering Data |
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PP: 1071-1089 |
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doi:10.18576/jsap/150408
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Author(s) |
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Mahmoud El-Morshedy,
M. H. Harpy,
Muhammad Ahsan-ul-Haq,
Mohammed Elgarhy,
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Abstract |
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| This paper introduces a new one-parameter continuous probability model, called the Unit ZLindley (UZL) distribution, for modeling observations restricted to the unit interval (0,1). The proposed model is constructed by applying the transformation Z = e−Y , where Y follows the ZLindley distribution. The resulting distribution possesses a simple analytical form and provides a flexible model for bounded data. Several statistical properties are investigated, including ordinary moments, central moments, conditional moments, moment generating function, characteristic function, mode, quantile function, Bowley skewness, Moore’s kurtosis, mean residual life, mean past life, Bonferroni curve, Lorenz curve, and entropy measures. Five estimation procedures, namely maximum likelihood, Anderson–Darling, Crame ́r–von Mises, ordinary least-squares, and weighted least-squares, are considered. A Monte Carlo simulation framework is developed to assess the finite-sample behavior of the proposed estimators under different parameter values and sample sizes. Finally, the usefulness of the UZL distribution is illustrated using two real datasets associated with the P3 and SC16 algorithms. The proposed distribution is compared with several existing unit-interval distributions using likelihood-based criteria and goodness-of- fit statistics. It is evident from the results that the UZL distribution offers a convenient choice to fit positively skewed data on the unit interval.
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