Pub Date : 2024-06-06DOI: 10.18187/pjsor.v20i2.4624
G. G. Hamedani, Amin Roshani
Certain characterizations of 26 recently introduced discrete distributions are presented in three directions: (i) based on an appropriate function of the random variable; (ii) in terms of the reverse hazard function and (iii) in terms of the hazard function.
{"title":"Characterizations of the Recently Introduced Discrete Distributions","authors":"G. G. Hamedani, Amin Roshani","doi":"10.18187/pjsor.v20i2.4624","DOIUrl":"https://doi.org/10.18187/pjsor.v20i2.4624","url":null,"abstract":"Certain characterizations of 26 recently introduced discrete distributions are presented in three directions: (i) based on an appropriate function of the random variable; (ii) in terms of the reverse hazard function and (iii) in terms of the hazard function.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141377451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.18187/pjsor.v20i2.3845
Anwar Hassan, I. H. Dar, M. A. Lone
In this manuscript, we introduced a new class of probability distributions called new exponentiated transformation(NET) that adds more flexibility to any baseline distribution without adding the complexity of an extra parameter. NET is then specialised on exponentiated exponential distribution and a new exponentiated exponential( NEE) distribution is obtained. The NEE distribution has wider flexibility in terms of density function and also has increasing, decreasing and bathtub hazard rate function. Several mathematical properties of NEE distribution are also highlighted. For applicability of proposed distribution, two engineering data sets are considered and it is sensed that NEE leads to a better fit than all models taken under consideration
在本手稿中，我们引入了一类新的概率分布，称为新指数变换（NET），它在不增加额外参数复杂性的情况下，为任何基线分布增加了更多灵活性。然后，我们在指数化指数分布上对 NET 进行了特殊化，得到了新指数化指数分布（NEE）。NEE 分布在密度函数方面具有更广泛的灵活性，而且还具有递增、递减和浴缸危险率函数。此外，还强调了 NEE 分布的几个数学特性。为了适用所提出的分布，我们考虑了两个工程数据集，结果发现 NEE 比所考虑的所有模型拟合得更好。
{"title":"A new class of probability distributions with an application in engineering science","authors":"Anwar Hassan, I. H. Dar, M. A. Lone","doi":"10.18187/pjsor.v20i2.3845","DOIUrl":"https://doi.org/10.18187/pjsor.v20i2.3845","url":null,"abstract":"In this manuscript, we introduced a new class of probability distributions called new exponentiated transformation(NET) that adds more flexibility to any baseline distribution without adding the complexity of an extra parameter. NET is then specialised on exponentiated exponential distribution and a new exponentiated exponential( NEE) distribution is obtained. The NEE distribution has wider flexibility in terms of density function and also has increasing, decreasing and bathtub hazard rate function. Several mathematical properties of NEE distribution are also highlighted. For applicability of proposed distribution, two engineering data sets are considered and it is sensed that NEE leads to a better fit than all models taken under consideration","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141383703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.18187/pjsor.v20i2.4535
H. Yousof, M. Saber, Abdullah H. Al-nefaie, Nadeem Shafique Butt, M. Ibrahim, Salwa L. Alkhayyat
This paper showcases the effectiveness of the discrete generalized Burr-Hatke distribution in analyzing insurance claims data, specifically focusing on scenarios with over-dispersed and zero-inflated claims. Key contributions include presenting foundational statistical theories with mathematical proofs to enrich the paper’s mathematical and statistical aspects. Through the application of this discrete distribution, the study conducted a thorough risk analysis across five diverse sets of insurance claims data, evaluating critical risk indicators at specified quantiles. These indicators provided detailed insights into potential losses across different risk levels, supporting effective risk management strategies. The research emphasizes the importance of selecting appropriate probability distributions when analyzing zero-inflated data, as commonly observed in insurance claims. The discrete distribution accommodated these unique data characteristics and facilitated a robust analysis of risk metrics, enhancing the accuracy of potential loss assessments and reducing associated uncertainties. Furthermore, the study highlights the practical relevance of the discrete distribution in addressing specific challenges inherent to insurance claims data. By leveraging this distribution, insurers and risk analysts can improve their risk modeling capabilities, leading to more informed decision-making and enhanced financial exposure management.
{"title":"A discrete claims-model for the inflated and over-dispersed automobile claims frequencies data: Applications and actuarial risk analysis","authors":"H. Yousof, M. Saber, Abdullah H. Al-nefaie, Nadeem Shafique Butt, M. Ibrahim, Salwa L. Alkhayyat","doi":"10.18187/pjsor.v20i2.4535","DOIUrl":"https://doi.org/10.18187/pjsor.v20i2.4535","url":null,"abstract":"This paper showcases the effectiveness of the discrete generalized Burr-Hatke distribution in analyzing insurance claims data, specifically focusing on scenarios with over-dispersed and zero-inflated claims. Key contributions include presenting foundational statistical theories with mathematical proofs to enrich the paper’s mathematical and statistical aspects. Through the application of this discrete distribution, the study conducted a thorough risk analysis across five diverse sets of insurance claims data, evaluating critical risk indicators at specified quantiles. These indicators provided detailed insights into potential losses across different risk levels, supporting effective risk management strategies. The research emphasizes the importance of selecting appropriate probability distributions when analyzing zero-inflated data, as commonly observed in insurance claims. The discrete distribution accommodated these unique data characteristics and facilitated a robust analysis of risk metrics, enhancing the accuracy of potential loss assessments and reducing associated uncertainties. Furthermore, the study highlights the practical relevance of the discrete distribution in addressing specific challenges inherent to insurance claims data. By leveraging this distribution, insurers and risk analysts can improve their risk modeling capabilities, leading to more informed decision-making and enhanced financial exposure management.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141386154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.18187/pjsor.v20i2.4411
Asuman Yılmaz, Mahmut Kara
Order statistics occupy an important place in statistical theory. They have an important place in many fields of applied statistics such as goodness of fit tests and parameter estimation. In addition, it is necessary to find the expected values of these order statistics in these application areas. However for some probability distributions, these expected values are very difficult to find such as the standard normal distribution. So the problem of finding the expected values of the order statistics in statistical theory is of importance. In this study, two novel approximation methods are proposed for the expected values of the order statistics of the standard normal distribution. Also, the true values with previously given approximations, simulation results and our proposed approximations are compared by using mean square error (MSE), mean absolute error (MAE) and maximum error (ME) criteria. Furthermore, to evaluate the performances of all approximation methods, we compute the differences between exact values and approximation values. Then, the plot of these differences against the exact values is given. Based on both the plots and the comparison results, novel approximations fit the true values better than the other approximations presented in this paper.
{"title":"Approximations to the Moments of Order Statistics for Normal Distribution","authors":"Asuman Yılmaz, Mahmut Kara","doi":"10.18187/pjsor.v20i2.4411","DOIUrl":"https://doi.org/10.18187/pjsor.v20i2.4411","url":null,"abstract":"Order statistics occupy an important place in statistical theory. They have an important place in many fields of applied statistics such as goodness of fit tests and parameter estimation. In addition, it is necessary to find the expected values of these order statistics in these application areas. However for some probability distributions, these expected values are very difficult to find such as the standard normal distribution. So the problem of finding the expected values of the order statistics in statistical theory is of importance. In this study, two novel approximation methods are proposed for the expected values of the order statistics of the standard normal distribution. Also, the true values with previously given approximations, simulation results and our proposed approximations are compared by using mean square error (MSE), mean absolute error (MAE) and maximum error (ME) criteria. Furthermore, to evaluate the performances of all approximation methods, we compute the differences between exact values and approximation values. Then, the plot of these differences against the exact values is given. Based on both the plots and the comparison results, novel approximations fit the true values better than the other approximations presented in this paper.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141384366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.18187/pjsor.v20i2.4458
Thatayaone Moakofi, B. Oluyede, B. Tlhaloganyang, Agolame Puoetsile
In this article, we introduce a robust generalization of the generalized Topp-Leone-G (GEN-TL-G) family of distributions via the heavy-tailed technique. The distribution is named heavy-tailed generalized Topp-Leone-G (HT-GEN-TL-G) family of distributions. Statistical properties of the HT-GEN-TL-G family of distributions including reliability functions, quantile function, density expansion, moments, moment generating function, incomplete moments, Rényi entropy, distribution of order statistics are derived. Different estimation methods including Maximum Likelihood, Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, Cram'er-von Mises and Maximum Product of Spacing are utilized to estimate the unknown parameters of the new distribution, and a simulation study is used to compare the results of the estimation methods. Risk measures for this distribution were also developed and finally the effectiveness of this new family of distributions was demonstrated using applications to two real data sets.
{"title":"A New Family of Heavy-Tailed Generalized Topp-Leone-G Distributions with Application","authors":"Thatayaone Moakofi, B. Oluyede, B. Tlhaloganyang, Agolame Puoetsile","doi":"10.18187/pjsor.v20i2.4458","DOIUrl":"https://doi.org/10.18187/pjsor.v20i2.4458","url":null,"abstract":"In this article, we introduce a robust generalization of the generalized Topp-Leone-G (GEN-TL-G) family of distributions via the heavy-tailed technique. The distribution is named heavy-tailed generalized Topp-Leone-G (HT-GEN-TL-G) family of distributions. Statistical properties of the HT-GEN-TL-G family of distributions including reliability functions, quantile function, density expansion, moments, moment generating function, incomplete moments, Rényi entropy, distribution of order statistics are derived. Different estimation methods including Maximum Likelihood, Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, Cram'er-von Mises and Maximum Product of Spacing are utilized to estimate the unknown parameters of the new distribution, and a simulation study is used to compare the results of the estimation methods. Risk measures for this distribution were also developed and finally the effectiveness of this new family of distributions was demonstrated using applications to two real data sets.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141383223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.18187/pjsor.v20i2.4409
M. Abdullah
Time series analysis plays a pivotal role in the strategic planning and risk management of reinsurance companies. It is an indispensable tool for gaining insights into the future utilization of reinsurance revenues. To effectively safeguard against substantial financial losses stemming from anticipated claims, reinsurance businesses must have a thorough understanding of the expected values of these claims. The ability to estimate the potential value of future claims is paramount, as it empowers reinsurance companies to proactively prepare and allocate resources, ensuring that they are well-equipped to cover likely future claims. Our research incorporates an innovative approach to estimate reinsurance revenues, leveraging the power of time series analysis. By applying the proposed paradigm to an original time series dataset, we aim to showcase its practical value and effectiveness in predicting future revenue trends. To assess the accuracy of these predictions, we employ the Box-Ljung statistical test, a statistical test commonly used in time series analysis. The corresponding p-value generated from this test provides a quantitative measure of the ability to analyze, capture and explain the underlying patterns in the data, thereby aiding reinsurance companies in providing an informed decisions and managing their financial risks effectively. In summary, the integration of time series analysis, single exponential smoothing (SEXS), and advanced forecasting techniques forms a critical foundation for enhancing the predictive capabilities of reinsurance businesses and ensuring their financial stability in the face of uncertain future claims.
时间序列分析在再保险公司的战略规划和风险管理中发挥着举足轻重的作用。它是深入了解再保险收入未来使用情况的不可或缺的工具。为了有效防范预期索赔带来的重大经济损失，再保险公司必须对这些索赔的预期价值有透彻的了解。估算未来索赔潜在价值的能力至关重要，因为它能让再保险公司积极主动地准备和分配资源，确保它们有足够的能力应对未来可能发生的索赔。我们的研究采用了一种创新方法，利用时间序列分析的力量来估算再保险收入。通过将提出的范式应用于原始时间序列数据集，我们旨在展示其在预测未来收入趋势方面的实用价值和有效性。为了评估这些预测的准确性，我们采用了 Box-Ljung 统计检验，这是一种常用于时间序列分析的统计检验方法。该检验所产生的相应 p 值可定量衡量分析、捕捉和解释数据中潜在模式的能力，从而帮助再保险公司做出明智决策并有效管理其财务风险。总之，将时间序列分析、单指数平滑法（SEXS）和先进的预测技术相结合，为提高再保险业务的预测能力、确保其在未来不确定的理赔情况下的财务稳定性奠定了重要基础。
{"title":"Using the Single-Exponential-Smoothing Time Series Model under the Additive Holt-Winters Algorithm with Decomposition and Residual Analysis to Forecast the Reinsurance-Revenues Dataset","authors":"M. Abdullah","doi":"10.18187/pjsor.v20i2.4409","DOIUrl":"https://doi.org/10.18187/pjsor.v20i2.4409","url":null,"abstract":"Time series analysis plays a pivotal role in the strategic planning and risk management of reinsurance companies. It is an indispensable tool for gaining insights into the future utilization of reinsurance revenues. To effectively safeguard against substantial financial losses stemming from anticipated claims, reinsurance businesses must have a thorough understanding of the expected values of these claims. The ability to estimate the potential value of future claims is paramount, as it empowers reinsurance companies to proactively prepare and allocate resources, ensuring that they are well-equipped to cover likely future claims. Our research incorporates an innovative approach to estimate reinsurance revenues, leveraging the power of time series analysis. By applying the proposed paradigm to an original time series dataset, we aim to showcase its practical value and effectiveness in predicting future revenue trends. To assess the accuracy of these predictions, we employ the Box-Ljung statistical test, a statistical test commonly used in time series analysis. The corresponding p-value generated from this test provides a quantitative measure of the ability to analyze, capture and explain the underlying patterns in the data, thereby aiding reinsurance companies in providing an informed decisions and managing their financial risks effectively. In summary, the integration of time series analysis, single exponential smoothing (SEXS), and advanced forecasting techniques forms a critical foundation for enhancing the predictive capabilities of reinsurance businesses and ensuring their financial stability in the face of uncertain future claims.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141386794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-05DOI: 10.18187/pjsor.v20i2.4461
Amal Alhejaili, Ateq A. Alghamedi
In certain situations probability computations are required for some complex distributions; like a compound distribution. This can leads to some comptational complexities. In such situations, the problem can be simplified by using some approximation techniques like the “saddle-point” approximation. In this paper, we have first proposed a compound bivariate distribution; namly the bivariate compound truncated Poisson-Gamma distribution; by compounding the zero truncated Poisson distribution with independent Gamma variates. The bivariate saddle-point approximation for the distribution function of the proposed distribution is obtained. An illustrative example for the approximate computation is given. An extensive simulatin study has been conducted to see the performance of the proposed saddle-point approximation for the distribution function of the bivariate compound truncated Poisson-Gamma distribution. It is found that the proposed saddle-point approximation is reasonably good to approximate the distribution function of the bivariate compound truncated Poisson-Gamma distribution.
{"title":"Approximation Methods for the Bivariate Compound Truncated Poisson Gamma Distribution","authors":"Amal Alhejaili, Ateq A. Alghamedi","doi":"10.18187/pjsor.v20i2.4461","DOIUrl":"https://doi.org/10.18187/pjsor.v20i2.4461","url":null,"abstract":"In certain situations probability computations are required for some complex distributions; like a compound distribution. This can leads to some comptational complexities. In such situations, the problem can be simplified by using some approximation techniques like the “saddle-point” approximation. In this paper, we have first proposed a compound bivariate distribution; namly the bivariate compound truncated Poisson-Gamma distribution; by compounding the zero truncated Poisson distribution with independent Gamma variates. The bivariate saddle-point approximation for the distribution function of the proposed distribution is obtained. An illustrative example for the approximate computation is given. An extensive simulatin study has been conducted to see the performance of the proposed saddle-point approximation for the distribution function of the bivariate compound truncated Poisson-Gamma distribution. It is found that the proposed saddle-point approximation is reasonably good to approximate the distribution function of the bivariate compound truncated Poisson-Gamma distribution.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141385268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.18187/pjsor.v20i1.4410
Saeed Adibfar, R. Noorossana
When a process is statistically under control, one may be interested in assessing the process performance based on the specification limits provided by the customer. This evaluation is referred to as process capability analysis. Manufacturing operations are often involved with multistage processes, in which the output of a stage is the input of its subsequent stage. This property is known as the cascade property. Existing methods in capability analysis studies are not applicable when a process or product is represented by profiles. This study presents a method to conduct process capability analysis in a multistage process when quality of a product or process is characterized by a simple linear profile. The performance of the proposed method for a two-stage process is evaluated by numerical simulation using an example from the literature. The results indicate that the proposed method eliminates the effect of the cascade property for different shift sizes and autocorrelations.
{"title":"Process Capability Analysis for Simple Linear Profiles in Multistage Processes","authors":"Saeed Adibfar, R. Noorossana","doi":"10.18187/pjsor.v20i1.4410","DOIUrl":"https://doi.org/10.18187/pjsor.v20i1.4410","url":null,"abstract":"When a process is statistically under control, one may be interested in assessing the process performance based on the specification limits provided by the customer. This evaluation is referred to as process capability analysis. Manufacturing operations are often involved with multistage processes, in which the output of a stage is the input of its subsequent stage. This property is known as the cascade property. Existing methods in capability analysis studies are not applicable when a process or product is represented by profiles. This study presents a method to conduct process capability analysis in a multistage process when quality of a product or process is characterized by a simple linear profile. The performance of the proposed method for a two-stage process is evaluated by numerical simulation using an example from the literature. The results indicate that the proposed method eliminates the effect of the cascade property for different shift sizes and autocorrelations.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140259673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.18187/pjsor.v20i1.4296
Kadir Karakaya, Ismail Kinaci, Yunus Akdoğan, Buğra Saraçoğlu, Coşkun Kuş
In quality engineering, process capability indexes are used to determine the capability of a process. The well-known of the process capability indexes are Cp, Cpk, Cpm, and Cpmk. These indexes assume the normality of the product lifetime. citet{maiti2010generalizing} suggested a Cpyk as a generalized process capability index without distributional assumption. In this paper, the maximum likelihood and Bayesian inference on the Cpyk are studied under progressive censoring when the underlying distribution is inverse Rayleigh distribution. Furthermore, Bayesian credible and highest posterior density intervals are discussed with the MCMC procedure. Several types of bootsrap confidence intervals are also considered. A Monte Carlo simulation is conducted in terms of the coverage probabilities and mean lengths of the proposed intervals. An illustrative example is presented to close the paper.
{"title":"Statistical Inference on Process Capability Index Cpyk for Inverse Rayleigh Distribution under Progressive Censoring","authors":"Kadir Karakaya, Ismail Kinaci, Yunus Akdoğan, Buğra Saraçoğlu, Coşkun Kuş","doi":"10.18187/pjsor.v20i1.4296","DOIUrl":"https://doi.org/10.18187/pjsor.v20i1.4296","url":null,"abstract":"In quality engineering, process capability indexes are used to determine the capability of a process. The well-known of the process capability indexes are Cp, Cpk, Cpm, and Cpmk. These indexes assume the normality of the product lifetime. citet{maiti2010generalizing} suggested a Cpyk as a generalized process capability index without distributional assumption. In this paper, the maximum likelihood and Bayesian inference on the Cpyk are studied under progressive censoring when the underlying distribution is inverse Rayleigh distribution. Furthermore, Bayesian credible and highest posterior density intervals are discussed with the MCMC procedure. Several types of bootsrap confidence intervals are also considered. A Monte Carlo simulation is conducted in terms of the coverage probabilities and mean lengths of the proposed intervals. An illustrative example is presented to close the paper. \u0000 ","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140259758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.18187/pjsor.v20i1.4307
Sirinapa Ayuyuen, W. Bodhisuwan
This article proposes the unit Garima (UGa) distribution for analysing proportion data. Some statistical properties of the UGa distribution are investigated, including survival and hazard functions, order statistics, quantile function, and stress-strength reliability measure. Next, a new family of continuous distributions, called the unit Garima-generated (UGa-G) family of distributions, is studied. The UGa-G family of distributions has the feature to use the UGa distribution as the main generator and the concept of the T-X family of distributions. Some UGa-G family sub-models are provided, such as the UGa-Beta, UGa-Weibull, and UGa-normal distributions. The maximum likelihood method is used to estimate the model parameters for the statistical aspect. A Monte Carlo simulation for the percentile bootstrap confidence intervals for each parameter of the proposed distributions is provided. Applications to eight practical data sets are given to demonstrate the usefulness of the proposed distributions.
本文提出了用于分析比例数据的单位伽利玛（UGa）分布。文章研究了 UGa 分布的一些统计性质，包括生存和危险函数、阶次统计、量化函数和应力强度可靠性度量。接下来，研究了一个新的连续分布族，称为单位伽利玛生成（UGa-G）分布族。UGa-G 分布族的特点是使用 UGa 分布作为主生成器，并具有 T-X 分布族的概念。还提供了一些 UGa-G 族子模型，如 UGa-Beta、UGa-Weibull 和 UGa-normal 分布。使用最大似然法估计统计方面的模型参数。蒙特卡罗模拟提供了拟议分布各参数的百分位数引导置信区间。还给出了八个实际数据集的应用，以证明所建议的分布的实用性。
{"title":"A generating family of unit-Garima distribution: Properties, likelihood inference, and application","authors":"Sirinapa Ayuyuen, W. Bodhisuwan","doi":"10.18187/pjsor.v20i1.4307","DOIUrl":"https://doi.org/10.18187/pjsor.v20i1.4307","url":null,"abstract":"This article proposes the unit Garima (UGa) distribution for analysing proportion data. Some statistical properties of the UGa distribution are investigated, including survival and hazard functions, order statistics, quantile function, and stress-strength reliability measure. Next, a new family of continuous distributions, called the unit Garima-generated (UGa-G) family of distributions, is studied. The UGa-G family of distributions has the feature to use the UGa distribution as the main generator and the concept of the T-X family of distributions. Some UGa-G family sub-models are provided, such as the UGa-Beta, UGa-Weibull, and UGa-normal distributions. The maximum likelihood method is used to estimate the model parameters for the statistical aspect. A Monte Carlo simulation for the percentile bootstrap confidence intervals for each parameter of the proposed distributions is provided. Applications to eight practical data sets are given to demonstrate the usefulness of the proposed distributions.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140258998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：