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Characterizations of the Recently Introduced Discrete Distributions 最近引入的离散分布的特征
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-06-06 DOI: 10.18187/pjsor.v20i2.4624
G. G. Hamedani, Amin Roshani
{"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}
引用次数: 0
A new class of probability distributions with an application in engineering science 一类新的概率分布在工程科学中的应用
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-06-05 DOI: 10.18187/pjsor.v20i2.3845
Anwar Hassan, I. H. Dar, M. A. Lone
{"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}
引用次数: 0
A discrete claims-model for the inflated and over-dispersed automobile claims frequencies data: Applications and actuarial risk analysis 针对夸大和过度分散的汽车索赔频率数据的离散索赔模型：应用与精算风险分析
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-06-05 DOI: 10.18187/pjsor.v20i2.4535
H. Yousof, M. Saber, Abdullah H. Al-nefaie, Nadeem Shafique Butt, M. Ibrahim, Salwa L. Alkhayyat
{"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}
引用次数: 0
Approximations to the Moments of Order Statistics for Normal Distribution 正态分布阶次统计量的近似值
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-06-05 DOI: 10.18187/pjsor.v20i2.4411
Asuman Yılmaz, Mahmut Kara
{"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}
引用次数: 0
A New Family of Heavy-Tailed Generalized Topp-Leone-G Distributions with Application 重尾广义 Topp-Leone-G 分布新家族及其应用
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-06-05 DOI: 10.18187/pjsor.v20i2.4458
Thatayaone Moakofi, B. Oluyede, B. Tlhaloganyang, Agolame Puoetsile
{"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}
引用次数: 0
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 使用加性霍尔特-温特斯算法下的单指数平滑时间序列模型与分解和残差分析来预测再保险收入数据集
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-06-05 DOI: 10.18187/pjsor.v20i2.4409
M. Abdullah
{"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}
引用次数: 0
Approximation Methods for the Bivariate Compound Truncated Poisson Gamma Distribution 双变量复合截断泊松伽玛分布的近似方法
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-06-05 DOI: 10.18187/pjsor.v20i2.4461
Amal Alhejaili, Ateq A. Alghamedi
{"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}
引用次数: 0
Process Capability Analysis for Simple Linear Profiles in Multistage Processes 多级工艺中简单线性轮廓的工艺能力分析
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-03-07 DOI: 10.18187/pjsor.v20i1.4410
Saeed Adibfar, R. Noorossana
{"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}
引用次数: 1
Statistical Inference on Process Capability Index Cpyk for Inverse Rayleigh Distribution under Progressive Censoring 渐进删减下反瑞利分布过程能力指数 Cpyk 的统计推断
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-03-07 DOI: 10.18187/pjsor.v20i1.4296
Kadir Karakaya, Ismail Kinaci, Yunus Akdoğan, Buğra Saraçoğlu, Coşkun Kuş
{"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}
引用次数: 0
A generating family of unit-Garima distribution: Properties, likelihood inference, and application 单位伽利玛分布的生成族：特性、似然法推理及应用
IF 1.5
Pakistan Journal of Statistics and Operation Research Pub Date : 2024-03-07 DOI: 10.18187/pjsor.v20i1.4307
Sirinapa Ayuyuen, W. Bodhisuwan
{"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}
引用次数: 0
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