Research Article A New Double Truncated Generalized Gamma Model with Some Applications Awad A. Bakery , 1,2 Wael Zakaria , 2 and OM Kalthum S. K. Mohamed 1,3 1 University of Jeddah, College of Science and Arts at Khulis, Department of Mathematics, Jeddah, Saudi Arabia 2 Department of Mathematics, Faculty of Science, Ain Shams University, P.O. Box 1156, Abbassia, Cairo 11566, Egypt 3 Academy of Engineering and Medical Sciences, Department of Mathematics, Khartoum, Sudan Correspondence should be addressed to OM Kalthum S. K. Mohamed; om_kalsoom2020@yahoo.com Received 7 May 2021; Accepted 6 August 2021; Published 17 August 2021 Academic Editor: Ghulam Mustafa Copyright © 2021 Awad A. Bakery 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. e generalized Gamma model has been applied in a variety of research fields, including reliability engineering and lifetime analysis. Indeed, we know that, from the above, it is unbounded. Data have a bounded service area in a variety of applications. A new five-parameter bounded generalized Gamma model, the bounded Weibull model with four parameters, the bounded Gamma model with four parameters, the bounded generalized Gaussian model with three parameters, the bounded exponential model with three parameters, and the bounded Rayleigh model with two parameters, is presented in this paper as a special case. is approach to the problem, which utilizes a bounded support area, allows for a great deal of versatility in fitting various shapes of observed data. Numerous properties of the proposed distribution have been deduced, including explicit expressions for the moments, quantiles, mode, moment generating function, mean variance, mean residual lifespan, and entropies, skewness, kurtosis, hazard function, survival function, r th order statistic, and median distributions. e delivery has hazard frequencies that are monotonically increasing or declining, bathtub-shaped, or upside-down bathtub-shaped. We use the Newton Raphson approach to approximate model parameters that increase the log-likelihood function and some of the parameters have a closed iterative structure. Six actual data sets and six simulated data sets were tested to demonstrate how the proposed model works in reality. We illustrate why the Model is more stable and less affected by sample size. Additionally, the suggested model for wavelet histogram fitting of images and sounds is very accurate. 1. Introduction e gamma (ΓM) model, including Weibull, gamma, ex- ponential, and Rayleigh as special submodels, among others, is a very popular distribution for modeling lifetime data and for modeling phenomenon with monotone failure rates. An advantage of ΓM is that it requires a little measure of parameters for learning. Also, these parameters can be measured by getting the expectation maximization (EM) algorithm [1, 2] to maximize the log-likelihood function. e early generalization of gamma distribution can be traced back to Amoroso [3] who discussed a generalized gamma distribution and applied it to fit income rates. Johnson et al. [4] gave a four parameter generalized gamma distribution which reduces to the generalized gamma distribution defined by Stacy [2] when the location pa- rameter is set to zero. Mudholkar and Srivastava [5] in- troduced the exponentiated method to derive a distribution. e generalized gamma defined by Stacy [2] is a three-parameter exponentiated gamma distribution. Agarwal and Al-Saleh [6] applied generalized gamma to study hazard rates. Balakrishnan and Peng [7] applied this distribution to develop generalized gamma frailty model. Cordeiro et al. [8] derived another generalization of Stacys generalized gamma distribution using exponentiated method and applied it to life time and survival analysis. Nadarajah and Gupta [9] proposed another type of gen- eralized gamma distribution with application to fit drought Hindawi Journal of Mathematics Volume 2021, Article ID 5500631, 27 pages https://doi.org/10.1155/2021/5500631