81 research outputs found
Advancing Continuous Distribution Generation: An Exponentiated Odds Ratio Generator Approach
This paper presents a new methodology for generating continuous statistical
distributions, integrating the exponentiated odds ratio within the framework of
survival analysis. This new method enhances the flexibility and adaptability of
distribution models to effectively address the complexities inherent in
contemporary datasets. The core of this advancement is illustrated by
introducing a particular subfamily, the "Type-2 Gumbel Weibull-G Family of
Distributions." We provide a comprehensive analysis of the mathematical
properties of these distributions, encompassing statistical properties such as
density functions, moments, hazard rate and quantile functions, R\'enyi
entropy, order statistics, and the concept of stochastic ordering. To establish
the robustness of our approach, we apply five distinct methods for parameter
estimation. The practical applicability of the Type-2 Gumbel Weibull-G
distributions is further supported through the analysis of three real-world
datasets. These empirical applications illustrate the exceptional statistical
precision of our distributions compared to existing models, thereby reinforcing
their significant value in both theoretical and practical statistical
applications
Another Generalized Transmuted Family of Distributions: Properties and Applications
We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Another generalized transmuted family of distributions. We present some special models. We investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating functions, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Renyi entropies and order statistics, which hold for any baseline model, certain characterisations are presented. Further, we introduce a bivariate extensions of the new family. We discuss the dierent method of estimation of the model parameters and illustrate the potentiality of the family by means of two applications to real data. A brief simulation for evaluating Maximum likelihood estimator is done
Generalized Transmuted Family of Distributions: Properties and Applications
We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and R´enyi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new family. We discuss the different methods of estimation of the model parameters and illustrate the potential application of the model via real data. A brief simulation for evaluating Maximum likelihood estimator is done. Finally certain characterziations of our model are presented
Exponentiated Exponential Lomax Distribution and its Properties
This research study the generalization of exponentiated version of Exponential lomax Distribution (ELD) called Exponentiated exponential lomax distribution (EEPD) through its distribution function and mathematical derivation of their moment, reliability, cumulative distribution function, Renyi Entropy and hazard rate function, Median, Quartile and Quantile Function. The distribution was found to generalize some known distributions thereby providing a great flexibility in modeling heavy tailed, skewed and bimodal distributions. Keywords: Exponentiated-exponential Lomax Distribution (EELD), Moment generating function, Hazard Function, Entropy, Median, Quartile, Quantile Function.DOI: 10.7176/MTM/9-1-0
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