Abstract
The 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. This 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. The 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.
Highlights
Academic Editor: Ghulam Mustafa e generalized Gamma model has been applied in a variety of research fields, including reliability engineering and lifetime analysis
Chen et al [10] used generalized gamma distribution with three parameters for flood frequency analysis, Zhao et al [11] used generalized gamma distribution with three parameters to give the statistical characterizes of high-resolution SAR images, and Mead et al [12] defined modified generalized gamma distribution so as to investigate greater flexibility in modeling data from a practical viewpoint and they derived multifarious identities and properties of this distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean deviation, mean residual lifetime, and expression of the entropies
We investigate the various special models of the BGΓM as listed in Table 1. e survival function and hazard rate function for BGΓM are, respectively, given by
Summary
E generalized Gamma model has been applied in a variety of research fields, including reliability engineering and lifetime analysis. Chen et al [10] used generalized gamma distribution with three parameters for flood frequency analysis, Zhao et al [11] used generalized gamma distribution with three parameters to give the statistical characterizes of high-resolution SAR images, and Mead et al [12] defined modified generalized gamma distribution so as to investigate greater flexibility in modeling data from a practical viewpoint and they derived multifarious identities and properties of this distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean deviation, mean residual lifetime, and expression of the entropies. We introduce in this paper the high flexibility of a bounded generalized Gamma model with five parameters (BGΓM) for analyzing data. Is new distribution has a flexibility to fit any kind of observed data whose pdf is monotonically increasing, decreasing, bathtub, and upside down bathtub-shaped depending on the parameter values and bounded support regions.
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