Weighted Tail Random Variable: A Novel Framework with Stochastic Properties and Applications
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913859547168768 |
|---|---|
| author | Islam, Sarikul Gupta, Nitin |
| author_facet | Islam, Sarikul Gupta, Nitin |
| contents | This paper introduces a novel framework to construct the probability density function (PDF) of non-negative continuous random variables. The proposed framework uses two functions: one is the survival function (SF) of a non-negative continuous random variable, and the other is a weight function, which is an increasing and differentiable function satisfying some properties. The resulting random variable is referred to as the weighted tail random variable (WTRV) corresponding to the given random variable and the weight function. We investigate several reliability properties of the WTRV and establish various stochastic orderings between a random variable and its WTRV, as well as between two WTRVs. Using this framework, we construct a WTRV of the Kumaraswamy distribution. We conduct goodness-of-fit tests for two real-world datasets, applied to the Kumaraswamy distribution and its corresponding WTRV. The test results indicate that the WTRV offers a superior fit compared to the Kumaraswamy distribution, which demonstrates the utility of the proposed framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Tail Random Variable: A Novel Framework with Stochastic Properties and Applications Islam, Sarikul Gupta, Nitin Statistics Theory Applications 2020: Primary 62N05, 60E15, Secondary 62N02 This paper introduces a novel framework to construct the probability density function (PDF) of non-negative continuous random variables. The proposed framework uses two functions: one is the survival function (SF) of a non-negative continuous random variable, and the other is a weight function, which is an increasing and differentiable function satisfying some properties. The resulting random variable is referred to as the weighted tail random variable (WTRV) corresponding to the given random variable and the weight function. We investigate several reliability properties of the WTRV and establish various stochastic orderings between a random variable and its WTRV, as well as between two WTRVs. Using this framework, we construct a WTRV of the Kumaraswamy distribution. We conduct goodness-of-fit tests for two real-world datasets, applied to the Kumaraswamy distribution and its corresponding WTRV. The test results indicate that the WTRV offers a superior fit compared to the Kumaraswamy distribution, which demonstrates the utility of the proposed framework. |
| title | Weighted Tail Random Variable: A Novel Framework with Stochastic Properties and Applications |
| topic | Statistics Theory Applications 2020: Primary 62N05, 60E15, Secondary 62N02 |
| url | https://arxiv.org/abs/2505.19824 |