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A Study of Conformable Fractional Inverse Weibull Model with Applications |
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PP: 279-291 |
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doi:10.18576/jsap/150209
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Author(s) |
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Ayat I. Al-Zoubi,
Shatha Hasan,
Mona Sakkijha,
Tariq Al-Hawary,
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Abstract |
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| This paper introduces the Conformable Fractional Inverse Weibull (CFIW) distribution, a novel extension of the classical inverse Weibull family through the incorporation of a conformable fractional operator. In this work, we develop a new model motivated by ideas that arise in fractional calculus and by observations encountered in reliability and survival studies. These areas often involve data that do not follow the usual scaling behavior, which encourages the construction of more flexible distributions. We present analytic form of the probability density function (PDF) of the CFIW. Then we derive expressions for the cumulative distribution function (CDF) in conformable fractional integral (CFI) sense. Reliability function, hazard rate, moment expressions are also derived. Conformable characteristic function and conformable moment generating function for CFIW distribution are obtained in the form of series representations involving the Gamma function. Mode, median and percentiles are also provided. We also introduce modified versions of three well-known entropy measures. Their behavior under the proposed model is examined through direct calculations and numerical illustrations. Moreover, parameter estimation via maximum likelihood is detailed, with numerical strategies for stable computation. A Monte Carlo simulation study with sample sizes n = {50,100,200,500} and 100 replications evaluates finite-sample bias and mean-square error (MSE) .
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