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A New Family of Transmuted Distribution with Application to Lifetime Data |
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PP: 1047-1072 |
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doi:10.18576/isl/120426
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Author(s) |
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Mohammed Ahmmed Mosilhy,
Hussein Eledum,
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Abstract |
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| In this article, a new family of the perspectives group of transmuted distributions called the MH-Transmuted Family of Distributions (MH-TD) is developed. MH-TD is confirmed in the quadratic (MH-QTD) and cubic (MH-CTD) distribution families. The new proposed family increases the flexibility of the transmuted distributions, enabling the modeling of diverse data sets in different fields of sciences, including engineering, environment, and finance. Based on the MH-QTD and MH-CTD maps, some new distributions are developed, including MH-Quadratic and MH-Cubic Transmuted Pareto distributions, MH-Quadratic and MH-Cubic Transmuted Gambel distributions, and MH-Quadratic and MH-Cubic Transmuted Fre ́chet distributions, explaining the probability density and distribution function for each distribution. Moreover, based on the MH-QTD and MH-CTD maps, two new generalizations of the exponential distributions called MH-quadratic transmuted exponential (MH-QTED) and MH-cubic transmuted exponential (MH-CTED) are proposed and studied in detail to explain the utility of the proposed family MH-Transmuted. Several statistical characteristics of the MH-QTED and MH-CTED are discussed, including the distribution and density functions, the moment-generating function, and the use of the maximum likelihood method to estimate the distributions’ parameters. Finally, the MH-QTED and MH-CTED models are fitted to a real-world, right-skewed dataset to determine their applicability.
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