Research Article Alpha Power Generalized Inverse Rayleigh Distribution: Its Properties and Applications Muhammad Ali, 1 Alamgir Khalil, 1 Zahra Almaspoor , 2 Sundus Hussain, 3 Umair Khalil, 4 and M. El-Morshedy 5,6 1 Department of Statistics, University of Peshawar, Peshawar, Pakistan 2 Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran 3 Department of Statistics, Shaheed Benazir Bhutto Women University, Peshawar, Pakistan 4 Department of Statistics, Abdul Wali Khan University Mardan, Mardan, Pakistan 5 Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia 6 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt Correspondence should be addressed to Zahra Almaspoor; z.almaspoor@stu.yazd.ac.ir Received 3 March 2022; Revised 26 April 2022; Accepted 30 April 2022; Published 7 June 2022 Academic Editor: Tahir Mehmood Copyright © 2022 Muhammad Ali et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is manuscript is related with the development of Alpha Power Generalized Inverse Rayleigh (APGIR) Distribution. e suggested model provides fit of life time data more efficiently. Some of the important characteristics of the suggested model are obtained including moments, moment generating function, quantile, mode, order statistics, stress-strength parameter, and entropies. Parameter estimates are obtained by MLE technique. e performance of the suggested model is evaluated using real-world data sets. e findings of the simulation and real data sets suggest that the newly proposed model is superior to other current competitor models. 1. Introduction Rayleigh distribution (RD) is a special model and a modified form of Weibull distribution when shape parameter equals 2. e RD has many applications in various disciplines including engineering and medical sciences, astronomy, and Physics. e RD has been well investigated in the literature. Some researchers have examined its significant properties [1–3]. Hoffman and Karst [4] studied characteristics of the RD and demonstrated how it can be used to analyze the responses of marine vehicles to wave excitation. Dyer and Whisenand [5] also demonstrated the use of RD in communication engineering. Polovko [6] showed how it can be applied to electro vacuum devices. ere are various variants of RD recently introduced by researchers that may be used for fitting of data more adequately. Voda [7] proposed generalized Rayleigh (GR) distribution. Voda [8, 9] obtained the ML estimates of the RD. Bhattacharya and Tyagi [10] used RD for the analysis of medical data. Gomes et al. [11] suggested Kumaraswamy generalized Rayleigh (KGR) distri- bution. Merovci [12] presented transmuted Rayleigh (TR) distribution for investigating lifetime data. Cordeiro et al. [13] developed beta generalized Rayleigh (BGR) distribution. ey also studied its main mathematical features. Leao et al. [14] proposed beta inverse Rayleigh (BIR) distribution. Ahmad et al. [15] offered transmuted inverse Rayleigh (TIR) distribution. Iriarte et al. [16] proposed slashed generalized Rayleigh (SGR) distribution. Lalitha and Mishra [17], Ariyawansa and Tem- pleton [18], Howlader and Hossain [19], Sinha and Howlader [20], and Abd Elfattah et al. [21] are just few among others who contributed to RD. Let X be a random variable having Rayleigh distribution. Symbolically, X ∼ R(θ). en, its CDF and PDF are f(x) 2θ 2 x exp −(θx) 2  x ≥ 0, θ > 0, F(x) 1 − exp −(θx) 2  x ≥ 0, θ > 0, (1) where θ represents scale parameter. Hindawi Mathematical Problems in Engineering Volume 2022, Article ID 7847110, 18 pages https://doi.org/10.1155/2022/7847110