A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution
This article proposes a solution to the problem of limiting the representation of three-stage phenomena to linear forms and addresses the stability of the second stage by introducing a novel distribution, the Fragmented Kumar-Trapez (FKT) distribution, which includes two additional parameters beyond...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/3/209 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849343236808638464 |
|---|---|
| author | Salma Omar Bleed Aisha A. Ben Taher Taha Radwan |
| author_facet | Salma Omar Bleed Aisha A. Ben Taher Taha Radwan |
| author_sort | Salma Omar Bleed |
| collection | DOAJ |
| description | This article proposes a solution to the problem of limiting the representation of three-stage phenomena to linear forms and addresses the stability of the second stage by introducing a novel distribution, the Fragmented Kumar-Trapez (FKT) distribution, which includes two additional parameters beyond the parameters used for an existing standard model. These parameters provide flexibility to the density function, enabling it to model a wide range of shapes. This work contributes to the understanding of distributions whose probability density functions are divided into three parts, addressing key questions such as: How to handle such distributions? How to estimate the range parameters of the trapezoidal and proposed distributions using the maximum likelihood method? How to estimate the unknown parameters of the proposed distribution using both maximum likelihood and Bayesian methods? In addition, the article explores some of the mathematical properties of the proposed distribution. Finally, a simulation study on generated data and an illustrated example are conducted to demonstrate the practical importance of the FKT distribution. WinBUGS 1.4 program is used to illustrate the application of MCMC simulation. |
| format | Article |
| id | doaj-art-9a5965d849ee4f8c847b948c8d493c6c |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-9a5965d849ee4f8c847b948c8d493c6c2025-08-20T03:43:02ZengMDPI AGAxioms2075-16802025-03-0114320910.3390/axioms14030209A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez DistributionSalma Omar Bleed0Aisha A. Ben Taher1Taha Radwan2Department of Statistics, College of Science, Al-Asmariya Islamic University, Zliten 218521, LibyaDepartment of Mathematical Sciences, Libyan Academy, Misrata 2449, LibyaDepartment of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi ArabiaThis article proposes a solution to the problem of limiting the representation of three-stage phenomena to linear forms and addresses the stability of the second stage by introducing a novel distribution, the Fragmented Kumar-Trapez (FKT) distribution, which includes two additional parameters beyond the parameters used for an existing standard model. These parameters provide flexibility to the density function, enabling it to model a wide range of shapes. This work contributes to the understanding of distributions whose probability density functions are divided into three parts, addressing key questions such as: How to handle such distributions? How to estimate the range parameters of the trapezoidal and proposed distributions using the maximum likelihood method? How to estimate the unknown parameters of the proposed distribution using both maximum likelihood and Bayesian methods? In addition, the article explores some of the mathematical properties of the proposed distribution. Finally, a simulation study on generated data and an illustrated example are conducted to demonstrate the practical importance of the FKT distribution. WinBUGS 1.4 program is used to illustrate the application of MCMC simulation.https://www.mdpi.com/2075-1680/14/3/209statistical modelBayesianfragmentedKumaraswamymaximum likelihoodMCMC algorithm |
| spellingShingle | Salma Omar Bleed Aisha A. Ben Taher Taha Radwan A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution Axioms statistical model Bayesian fragmented Kumaraswamy maximum likelihood MCMC algorithm |
| title | A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution |
| title_full | A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution |
| title_fullStr | A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution |
| title_full_unstemmed | A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution |
| title_short | A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution |
| title_sort | new flexible model for three stage phenomena the fragmented kumar trapez distribution |
| topic | statistical model Bayesian fragmented Kumaraswamy maximum likelihood MCMC algorithm |
| url | https://www.mdpi.com/2075-1680/14/3/209 |
| work_keys_str_mv | AT salmaomarbleed anewflexiblemodelforthreestagephenomenathefragmentedkumartrapezdistribution AT aishaabentaher anewflexiblemodelforthreestagephenomenathefragmentedkumartrapezdistribution AT taharadwan anewflexiblemodelforthreestagephenomenathefragmentedkumartrapezdistribution AT salmaomarbleed newflexiblemodelforthreestagephenomenathefragmentedkumartrapezdistribution AT aishaabentaher newflexiblemodelforthreestagephenomenathefragmentedkumartrapezdistribution AT taharadwan newflexiblemodelforthreestagephenomenathefragmentedkumartrapezdistribution |