Analytical results of the APTWE model and other competing models for the second data set.

Analytical results of the APTWE model and other competing models for the second data set.

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This paper considers three special cases: Exponential, Rayleigh and Lindley of a family of generalized distributions, called alpha power Weibull G (APW-G) family. Some essential and valuable statistical properties of the family of distributions are obtained. The proposed distributions are very flexible and can be used to model data with decreasing,...

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Citations

... Ref. Dey, Nassar, and Kumar (2019) developed the inverse Lindly distribution with APT. Ref. Ihtisham, Khalil, Manzoor, Khan, and Ali (2019) offered the APT Pareto distribution, for more see Ahmad, Elgarhy, and Abbas (2018), Elbatal, Ahmed, Elgarhy, and Almarashi (2019), Elbatal, Elgarhy, and Kibria (2021), Hassan, Elgarhy, Mohammed, and Alrajhi (2019). ...
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Alpha power transformed, Burr X family, Moments, Maximum likelihood estimation}, abstract = {In this paper, we discuss a new approach to statistical distributions that has been suggested and is termed the alpha power transformation Burr X family of distributions. The newly offered class of distributions is the mixing between the alpha power transformation and the Burr X class of distributions. This new class helps evaluate data from the real world because it is analytically possible and can be utilized. Many asymmetrical submodels were included in the newly proposed class of distributions. We offer four new submodels that belong to a new class of distributions. These submodels are referred to as the alpha power transformation Burr X exponential distribution, the alpha power transformation Burr X Rayleigh distribution, alpha power transformation Burr X Lindley distribution, and the alpha power transformation Burr X Weibull distribution. The expansion of the alpha power transformation Burr X-G density function was computed to obtain additional statistical characteristics of the newly suggested family of distributions. Several statistical attributes of the alpha power transformation Burr X-G class were obtained. These characteristics include a quantile function, ordinary moments, conditional moments, and moment-generating functions. Estimation of parameters is performed using the maximum likelihood estimation approach. An investigation of the simulation was conducted to evaluate the performance of the maximum likelihood estimation approach. Four data sets taken from the actual world related to radiotherapy, environmental, and engineering sciences were used to demonstrate the significance and application of the suggested family
... Due to the drawbacks of the WD, a number of variants of the distribution has been proposed in the literature with the goal of enhancing its modeling capabilities as well as making it suitable for specific modeling lifetime phenomena. There are some recent discussed variants, such as the exponentiated WD [4], transmuted additive WD [5], Kumaraswamy transmuted exponentiated modified WD [6], Topp-Leone Modified WD [7], Burr X exponentiated WD [8], Kavya-Manoharan exponentiated WD [9], Marshall-Olkin power-generalized WD [10], truncated Cauchy power Weibull-G [11], alpha power transformed Weibull-G [12], Weighted WD [13], exponentiated power generalized Weibull power series family [14], exponentiated truncated inverse Weibull-G [15], odd inverse power generalized WD [16], extended inverse WD [17], Weibull WD (WWD) [18], and exponentiated WWD [19]. However, it is still a challenge to develop a distribution that is well suited for modeling lifetime scenarios characterized by non-monotonic failure rates reflecting real-world situations where the failure rate of a system or component may vary over time. ...
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... Recently, (Elgarhy et al., 2018) introduced the type-II Topp-Leone-G family (TIITL-G), odds generalized exponential-G family by (Tahir et al., 2015), transmuted family by (Shaw & Buckley, 2009) and for more information see (Alyami et al., 2022a(Alyami et al., , 2022bChettri et al., 2022, pp. 511-535;Eghwerido et al., 2022;Elbatal et al., 2021). The cdf of the TIITL-G family of continuous distribution is provided by: ...
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... Several researchers have employed the transformation to obtain novel distributions produced by the APT-G of distributions. Ref. [55][56][57][58][59][60][61][62][63][64][65] proposed the APT Pareto, APT Weibull, APT Lindley, APT extended exponential, APT inverse Lindley, APT Topp-Leone Weibull, exponential APT-G, transmuted APT-G, APT extended power Lindley, APT Kumaraswamy-Burr III and APT Weibull-G distributions respectively. ...
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... Alpha-Power Exponentiated Inverse Rayleigh distribution and its application to real and simulated data by [11]. Alpha Power Transformed Weibull-G Family of Distributions: Theory and Applications by [12]. The Alpha Power Exponentiated Inverse Exponential distribution and its application to Italy's COVID-19 mortality rate data by [13], compared the new distribution with other distributions and it outperformed the other distributions. ...
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... By inserting (1) and (2) into (3) and (4) (5) and the associated density is obtained as: ...
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... Alpha Power Exponentiated Inverse Rayleigh distribution and its applications to real and simulated data by [15]. Alpha Power Transformed Weibull-G Family of Distributions: Theory and Applications by [16]. Alpha Power Inverted Exponential Distribution: Properties and Application by [17]. ...
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