Modified generalized Weibull distribution: theory and applications
Mustafa S. Shama,
Amirah Saeed Alharthi,
Fatimah A. Almulhim
et al.
Abstract:This article presents and investigates a modified version of the Weibull distribution that incorporates four parameters and can effectively represent a hazard rate function with a shape resembling a bathtub. Its significance in the fields of lifetime and reliability stems from its ability to model both increasing and decreasing failure rates. The proposed distribution encompasses several well-known models such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh, and modified Weibull dist… Show more
“…Here, various estimation techniques for determining the APCos-ME's parameters are covered. For additional information concerning the application of estimation techniques, see Alshawarbeh et al [4], Rahman et al [18], Rodrigues et al [23], Shama et al [28], and Almetwally and Meraou [2]. 4.1.…”
Section: Estimation Methods Of Apcos-me Modelmentioning
This article introduces a new model using the alpha power cosine transformed method for modeling complex data used in hydrology and engineering studies. The alpha power novel distribution transformed the cosine moment exponential model with two parameters. Its probability density function can be skewed and unimodal. Various statistical and mathematical properties are established, and the unknown parameters of the suggested model are determined using numerous estimation procedures. Also, the potential of these estimation techniques is calculated via some simulation studies. In the end, two real data sets are made using the proposed model to make a practical application in environmental and survival fields. The potential and utility of the recommended distribution are verified with other well known models and it shows great superiority in fitting the proposed data sets.
“…Here, various estimation techniques for determining the APCos-ME's parameters are covered. For additional information concerning the application of estimation techniques, see Alshawarbeh et al [4], Rahman et al [18], Rodrigues et al [23], Shama et al [28], and Almetwally and Meraou [2]. 4.1.…”
Section: Estimation Methods Of Apcos-me Modelmentioning
This article introduces a new model using the alpha power cosine transformed method for modeling complex data used in hydrology and engineering studies. The alpha power novel distribution transformed the cosine moment exponential model with two parameters. Its probability density function can be skewed and unimodal. Various statistical and mathematical properties are established, and the unknown parameters of the suggested model are determined using numerous estimation procedures. Also, the potential of these estimation techniques is calculated via some simulation studies. In the end, two real data sets are made using the proposed model to make a practical application in environmental and survival fields. The potential and utility of the recommended distribution are verified with other well known models and it shows great superiority in fitting the proposed data sets.
“…It is often applied to predict the life of LED light sources prone to stress failures, such as lead fracture, solder joint failure, and chemical corrosion. The Weibull distribution (Shama et al, 2023), a continuous probability distribution with roots in statistics, provides great flexibility and extensive applicability. Figure 2C displays the Weibull distribution probability density diagram, with β = 1 and α adjusted to various values, exhibiting characteristics resembling the logarithmic and exponential normal distributions when α ≤ 1, and resembling the γ distribution when α > 1.5.…”
Life prediction significantly influences the reliability of LED light sources. While high-power LED light sources theoretically offer a lifespan of up to 100,000 h, irreversible damage to components leads to light failure, substantially reducing their actual lifespan. Consequently, accurate life prediction is pivotal for manufacturers to cut costs and enhance economic efficiency. This necessity aligns with the interests of communities, governments, and consumers. Currently, the most extensively employed prediction methods are based on traditional physical models and data-driven approaches. The focal point of current research lies in realizing model fusion, presenting both a hotspot and a challenge. To elucidate the relationships, advantages, and disadvantages of different algorithms and establish the groundwork for LED life prediction algorithm development, this paper first introduces material properties and the light decay model of high-power LED light sources. Subsequently, it discusses the principles and methods of the physical model concerning light source reliability. The paper also presents a review and comparison of recent domestic and foreign light source life prediction models. Finally, it provides insights into the expected future development trends in life prediction.
“…In this context, statistical distributions play a crucial role in allowing statisticians and practitioners to make predictions and draw conclusions across a wide range of fields of study. The Inverse Lomax distribution and Weibull distribution are two commonly used distributions that have different interpretations and uses but can be studied jointly in specific contexts to yield more comprehensive insights ( [6], [7], [8], [9], and [10]).…”
A new family of distributions called Inverse Lomax Weibull G (ILWG) based on the Inverse Lomax G by [1] and Weibull G by [2] was proposed. Exponential distribution was used as a member of this family to demonstrate the applicability of the new family. Some statistical properties of the Inverse Lomax Weibull exponential distribution (ILWED) were demonstrated. Sample quantiles were presented. A simulation study was also presented. Lastly, an application to Bladder Cancer data was demonstrated based on the ILWED.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.