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TRANSMUTED X-RAMA DISTRIBUTION: PROPERTIES AND APPLICATIONS.

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Title: TRANSMUTED X-RAMA DISTRIBUTION: PROPERTIES AND APPLICATIONS.
Authors: GEORGE, NIMMY1 nimmygeorge60@gmail.com, SINDHU E. S.1 sindhujaimon@kecollege.ac.in
Source: Reliability: Theory & Applications. Dec2025, Vol. 20 Issue 4, p304-317. 14p.
Subjects: Probability density function, Cumulative distribution function, Hazard function (Statistics), Statistical reliability, Maximum likelihood statistics, Least squares, Uncertainty (Information theory), Distribution (Probability theory)
Abstract: In this paper, we introduce a new generalized distribution called Transmuted X-Rama distribution (TXRD) by using the quadratic rank transmutation map (QRTM). The probability density function (PDF), cumulative distribution function (CDF), and key moments of the transmuted distribution are meticulously derived to demonstrate how the transmutation parameter influences the shape of the distribution. Additionally, we analyze its reliability function, hazard rate, odds function, entropy and order statistics all of which are crucial in applications involving uncertainty and longevity data. We propose the method of maximum likelihood estimation (MLE) and method of least squares estimation (LSE) for the estimation of parameters of the distribution. We also show how the transmuted distribution may be fitted to real datasets. [ABSTRACT FROM AUTHOR]
Copyright of Reliability: Theory & Applications is the property of International Group on Reliability and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: In this paper, we introduce a new generalized distribution called Transmuted X-Rama distribution (TXRD) by using the quadratic rank transmutation map (QRTM). The probability density function (PDF), cumulative distribution function (CDF), and key moments of the transmuted distribution are meticulously derived to demonstrate how the transmutation parameter influences the shape of the distribution. Additionally, we analyze its reliability function, hazard rate, odds function, entropy and order statistics all of which are crucial in applications involving uncertainty and longevity data. We propose the method of maximum likelihood estimation (MLE) and method of least squares estimation (LSE) for the estimation of parameters of the distribution. We also show how the transmuted distribution may be fitted to real datasets. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Reliability: Theory & Applications is the property of International Group on Reliability and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        Type: general
      – SubjectFull: Cumulative distribution function
        Type: general
      – SubjectFull: Hazard function (Statistics)
        Type: general
      – SubjectFull: Statistical reliability
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      – SubjectFull: Maximum likelihood statistics
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      – SubjectFull: Least squares
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      – SubjectFull: Uncertainty (Information theory)
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      – SubjectFull: Distribution (Probability theory)
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              M: 12
              Text: Dec2025
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