Estimation of the coefficients of variation for inverse power Lomax distribution
One useful descriptive metric for measuring variability in applied statistics is the coefficient of variation (CV) of a distribution. However, it is uncommon to report conclusions about the CV of non-normal distributions. This study develops a method for estimating the CV for the inverse power Lomax...
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241595 |
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| author | Samah M. Ahmed Abdelfattah Mustafa |
| author_facet | Samah M. Ahmed Abdelfattah Mustafa |
| author_sort | Samah M. Ahmed |
| collection | DOAJ |
| description | One useful descriptive metric for measuring variability in applied statistics is the coefficient of variation (CV) of a distribution. However, it is uncommon to report conclusions about the CV of non-normal distributions. This study develops a method for estimating the CV for the inverse power Lomax (IPL) distribution using adaptive Type-Ⅱ progressive censored data. The experiment is a well-liked plan for gathering data, particularly for a very dependable product. The point and interval estimate of CV are formulated under the classical approach (maximum likelihood and bootstrap) and the Bayesian approach with respect to the symmetric loss function. For the unknown parameters, the joint prior density is calculated using the Bayesian technique as a product of three independent gamma densities. Additionally, it is recommended to use the Markov Chain Monte Carlo (MCMC) method to calculate the Bayes estimate and generate posterior distributions. A simulation study and a numerical example are given to assess the performance of the maximum likelihood and Bayes estimations. |
| format | Article |
| id | doaj-art-79ea40942e304b4298a423ac2924badd |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-79ea40942e304b4298a423ac2924badd2025-01-23T07:53:24ZengAIMS PressAIMS Mathematics2473-69882024-11-01912334233344110.3934/math.20241595Estimation of the coefficients of variation for inverse power Lomax distributionSamah M. Ahmed0Abdelfattah Mustafa1Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, EgyptMathematics Department, Faculty of Science, Islamic University of Madinah, Madinah 42351, KSAOne useful descriptive metric for measuring variability in applied statistics is the coefficient of variation (CV) of a distribution. However, it is uncommon to report conclusions about the CV of non-normal distributions. This study develops a method for estimating the CV for the inverse power Lomax (IPL) distribution using adaptive Type-Ⅱ progressive censored data. The experiment is a well-liked plan for gathering data, particularly for a very dependable product. The point and interval estimate of CV are formulated under the classical approach (maximum likelihood and bootstrap) and the Bayesian approach with respect to the symmetric loss function. For the unknown parameters, the joint prior density is calculated using the Bayesian technique as a product of three independent gamma densities. Additionally, it is recommended to use the Markov Chain Monte Carlo (MCMC) method to calculate the Bayes estimate and generate posterior distributions. A simulation study and a numerical example are given to assess the performance of the maximum likelihood and Bayes estimations.https://www.aimspress.com/article/doi/10.3934/math.20241595gibbs and metropolis samplerinverse power lomax distributionadaptive type-ⅱ progressive censoring schemecoefficient of variationbayesian approach |
| spellingShingle | Samah M. Ahmed Abdelfattah Mustafa Estimation of the coefficients of variation for inverse power Lomax distribution AIMS Mathematics gibbs and metropolis sampler inverse power lomax distribution adaptive type-ⅱ progressive censoring scheme coefficient of variation bayesian approach |
| title | Estimation of the coefficients of variation for inverse power Lomax distribution |
| title_full | Estimation of the coefficients of variation for inverse power Lomax distribution |
| title_fullStr | Estimation of the coefficients of variation for inverse power Lomax distribution |
| title_full_unstemmed | Estimation of the coefficients of variation for inverse power Lomax distribution |
| title_short | Estimation of the coefficients of variation for inverse power Lomax distribution |
| title_sort | estimation of the coefficients of variation for inverse power lomax distribution |
| topic | gibbs and metropolis sampler inverse power lomax distribution adaptive type-ⅱ progressive censoring scheme coefficient of variation bayesian approach |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241595 |
| work_keys_str_mv | AT samahmahmed estimationofthecoefficientsofvariationforinversepowerlomaxdistribution AT abdelfattahmustafa estimationofthecoefficientsofvariationforinversepowerlomaxdistribution |