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A Bayesian Approach to Weibull Distribution with Application to Insurance Claims Data 威布尔分布的贝叶斯方法及其在保险索赔数据中的应用
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2023-05-15 DOI: 10.13052/jrss0974-8024.1611
H. Abubakar, Shamsul Rijal Muhammad Sabri
Statistical distributions are of great interest for actuaries in modelling and fitting the distribution of various data sets. It can be used to present a description of risk exposure on the investment, where the level of exposure to the risk can be determined by “key risk indicators” that usually are functions of the statistical model. Financial mathematicians and actuarial scientists often use such key risk indicators to determine the degree to which a particular company is subject to certain aspects of risk, which arise from changes in underlying variables such as prices of equity, interest rates fluctuations, or exchange rates. Weibull distribution is one of the most popular statistical distribution models employed by the actuarial and financial risk management problems in fitting and or in modelling the behaviours of financial data or lifetime event data to forecast stock pricing movement or uncertainly prediction. In this study, a Bayesian approach to the Weibull distribution model on the assumption of gamma prior to Weibull distribution parameters has been proposed. A computational study based on the actuarial measures is conducted, proving the proposed distribution of the claim amount. Along this line, in assessing the performance of the proposed method, the results of the simulations study have been conducted to explore the efficiency of the proposed estimators is compared to a maximum likelihood (MLE) and simulated annealing algorithm (SA). Finally, an actuarial real data set is analyzed, proving that the proposed model can be used effectively to model insurance claim data.
精算师对统计分布进行建模和拟合各种数据集的分布非常感兴趣。它可用于描述投资的风险敞口,其中风险敞口水平可由“关键风险指标”确定,这些指标通常是统计模型的函数。金融数学家和精算学家经常使用这些关键风险指标来确定特定公司在多大程度上受到某些方面的风险,这些风险源于股票价格、利率波动或汇率等基本变量的变化。威布尔分布是精算和金融风险管理问题中最流行的统计分布模型之一,用于拟合和/或建模金融数据或终身事件数据的行为,以预测股票定价变动或不确定性预测。在这项研究中,在假设伽马先于威布尔分布参数的情况下,提出了一种威布尔分布模型的贝叶斯方法。根据精算计量进行了计算研究,证明了索赔额的拟议分布。沿着这条线,在评估所提出的方法的性能时,已经进行了模拟研究的结果,以探索所提出的估计量的效率与最大似然(MLE)和模拟退火算法(SA)进行了比较。最后,对精算真实数据集进行了分析,证明了所提出的模型可以有效地用于保险索赔数据的建模。
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引用次数: 3
Performance Analysis of Continuous Casting System of Steel Industry 钢铁工业连铸系统性能分析
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2023-04-06 DOI: 10.13052/jrss0974-8024.15212
Sapna Saini, J. Kumar, M. S. Kadyan
The continuous casting system is the most important to solidify the liquid steel in the steel industry. Steel is the backbone of civilization and modernization. So, there is a need to optimize the performance of continuous casting system of steel industry. Continuous casting system has six subsystems: “Pouring turret ladle”, “Tundish”, “Mold”, “Water spray chamber”, “Support roller” and “Torch cutter”. Series configuration is used to arrange these subsystems. The subsystem “Pouring turret ladle” is having three similar units. These units are operating in parallel. The subsystems “Tundish”, “Mold”, “Water spray chamber” and “Support roller” have a single unit. The subsystem “Torch cutter” contains two identical units: one is operative and other keep in cold standby. For all subsystems, the distribution of repair rates and failure rates of continuous casting system are taken as arbitrary distributions. Analysis of continuous casting system has been done by using supplementary variable technique. The numerical results of reliability measure of continuous casting system in terms of availability and profit have been computed by assuming exponential, Rayleigh and Weibull distributions.
连铸系统是钢铁工业中最重要的凝固钢液的系统。钢铁是文明和现代化的支柱。因此,有必要对钢铁工业连铸系统的性能进行优化。连铸系统有六大子系统:“浇注转塔钢包”、“中间包”、“模具”、“喷水室”、“托辊”和“割炬”。这些子系统采用串联配置方式进行排列。“浇注炮塔钢包”子系统有三个类似的单元。这些单元并行运行。“中间包”、“模具”、“喷水室”和“托辊”子系统为一个单元。“火炬切割机”子系统包含两个相同的单元:一个是工作的,另一个保持冷备用。对于各子系统,将连铸系统的返修率和故障率的分布取为任意分布。采用补充变量法对连铸系统进行了分析。采用指数分布、瑞利分布和威布尔分布对连铸系统的可用性和效益进行了数值计算。
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引用次数: 0
A Semi-parametric NHPP-based Software Reliability Modeling with Local Polynomial Debug Rate 基于局部多项式调试率的半参数nhpp软件可靠性建模
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2023-04-06 DOI: 10.13052/jrss0974-8024.15215
Siqiao Li, T. Dohi, H. Okamura
In this paper, we propose a new non-homogeneous Poisson process (NHPP) based software reliability model (SRM), where the software debug rate is given by a local polynomial function. The main feature of this semi-parametric SRM is to control the goodness-of-fit by changing the polynomial degree. Numerical examples with 16 actual software development project data are devoted to comparing our SRM with the well-known existing NHPP-based SRMs in terms of goodness-of-fit and predictive performances.
本文提出了一种新的基于非齐次泊松过程(NHPP)的软件可靠性模型(SRM),其中软件调试率由一个局部多项式函数给出。这种半参数SRM的主要特点是通过改变多项式度来控制拟合优度。通过16个实际软件开发项目数据的数值示例,将我们的SRM与现有的基于nhpp的SRM在拟合优度和预测性能方面进行了比较。
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引用次数: 0
Reliability Index of Simply Supported Beam Based on HL Method 基于HL法的简支梁可靠性指标研究
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2023-04-06 DOI: 10.13052/jrss0974-8024.15214
M. Devi, T. Sumathi, Uma Maheshwari, A. Satyanarayana
In this paper, reliability of simply supported I-beam is studied under point load at the mid-point of span. Reliability index has been obtained by using Hasofer-Lind method. In the analysis, yield strength of material, depth of the section and load are considered as basic random variables and those are assumed to follow normal distribution. Non-linear limit state surface function has been considered. Derived design point in each case and found the reliability.
本文对跨度中点荷载作用下简支工字梁的可靠度进行了研究。采用hasfer - lind法得到了可靠性指标。在分析中,将材料屈服强度、截面深度和荷载作为基本随机变量,假设它们服从正态分布。考虑了非线性极限状态曲面函数。推导出每种情况下的设计点,求得可靠度。
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引用次数: 0
Accelerated Failure Time Models with Applications to Endometrial Cancer Survival Data 加速失效时间模型在子宫内膜癌生存数据中的应用
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2023-04-06 DOI: 10.13052/jrss0974-8024.15213
M. Tripathy, P. Swain, P. K. Sarangi, S. Pattnaik
The objective of this study is to determine the significant predictors of endometrial cancer using accelerated failure time models (AFTM). We have demonstrated the applications of AFTM viz. Exponential, Weibull, Log-normal, Log-logistic, Gompertz, Gamma and Generalized Gamma AFTM, as an alternative of Cox proportional hazard model. Data for the analysis was collected from Acharya Harihar Post Graduate Institute of Cancer (AHPGIC), Cuttack, Odisha during the period 2016–20. Based on the lowest Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) value, the Weibull AFTM has been chosen as the best fitted AFT model. The predictors such as age, comorbidity, tumor size, isolated para-aortic and adnexa have been found as significant predictors (p-value < 0.05) to explain the survival of endometrial cancer patients. Hence, by optimizing different treatments, based on such prognostic factors plays an important role in managing endometrial cancer at an early stage.
本研究的目的是利用加速失效时间模型(AFTM)确定子宫内膜癌的重要预测因素。我们展示了AFTM的应用,即指数、威布尔、对数正态、对数逻辑、Gompertz、Gamma和广义Gamma AFTM,作为Cox比例风险模型的替代。分析数据于2016 - 2020年期间从奥里萨邦卡塔克的阿查里亚哈里哈尔癌症研究生研究所(AHPGIC)收集。基于赤池信息准则(AIC)和贝叶斯信息准则(BIC)的最小值,选择威布尔AFTM作为最优拟合的AFT模型。年龄、合并症、肿瘤大小、分离的主动脉旁和附件是子宫内膜癌患者生存的重要预测因子(p值< 0.05)。因此,通过优化不同的治疗方法,基于这些预后因素在子宫内膜癌的早期治疗中起着重要作用。
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引用次数: 0
Linear Consecutive-k-out-of-n: G System Reliability Analysis 线性连续k-out-of-n:G系统可靠性分析
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2023-02-10 DOI: 10.13052/jrss0974-8024.15211
Garima Chopra, M. Ram
The concerned study pertains to the development of a new stochastic model for the reliability analysis of linear consecutive-k-out-of-n: G system, where k>n2. In the developed model, system may collapse as a result of common cause failure or hardware failure in its units. The system has exponentially distributed failure rates, and in case of breakdown, it is repaired with the copula method. The developed model has been examined through supplementary variable technique (SVT) along with Laplace transform. The current paper has specifically studied consecutive-(n-1)-out-of-n: G system. The performance of such system having ten components is explored and its various reliability measures have been obtained and discussed with the help of graphs. The originality of this work lies in incorporating common cause failure in conjunction with copula repair in the reliability modeling of consecutive systems through the SVT. The study confirms that an increase in failure rates and the number of components of the concerned system decreases mean time to failure (MTTF). The profit of linear consecutive-9-out-of-10: G system is examined with the help of a numerical example.
这项研究涉及开发一种新的随机模型,用于线性连续k-out-ofn-G系统的可靠性分析,其中k>n2。在所开发的模型中,系统可能会因其单元的共同原因故障或硬件故障而崩溃。该系统具有指数分布的故障率,在发生故障时,使用copula方法进行修复。通过补充变量技术(SVT)和拉普拉斯变换对所开发的模型进行了检验。本文专门研究了n:G中的连续(n-1)系统。探讨了这种由十个部件组成的系统的性能,并获得了它的各种可靠性指标,并借助图表进行了讨论。这项工作的独创性在于通过SVT将常见原因故障与copula修复结合在连续系统的可靠性建模中。该研究证实,故障率和相关系统组件数量的增加会降低平均故障时间(MTTF)。通过算例检验了线性连续系统的收益性。
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引用次数: 0
Bayesian and MLE of R=P(Y>X) for Exponential Distribution Based on Varied L Ranked Set Sampling 基于变L秩集抽样的指数分布R=P(Y>X)的Bayes和MLE
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-11-23 DOI: 10.13052/jrss0974-8024.15210
Mohamed S. Abdallah
The ranked set sampling (RSS) is an effective scheme popularly used to produce more precisely estimators. Despite its popularity, RSS suffers from some drawbacks which includes high sensitivity to outliers and it cannot sometimes be applicable when the population is relatively small. To overcome these limitations, varied L ranked set sampling (VLRSS) is recently introduced. It is shown that VLRSS scheme enjoys with many interesting properties over RSS and also encompasses several existing RSS schemes. In addition, it is also helpful for providing precise estimates of several population parameters. To fill this gap, this article extends the work and address the estimation of based ℛ on VLRSS when the strength and stress both follow exponential distribution. Maximum likelihood approach as well as Bayesian method are considered for estimating ℛ. The Bayes estimators are obtained by using gamma distribution under general entropy loss function and LINEX loss function. The performance of the estimators based on VLRSS are investigated by a simulation study as well as a real dataset relevant to industrial field. The results reveal that the proposed estimators are more efficient relative to their analogues estimators under L ranked set sampling given that the quality of ranking is fairly good.
排序集抽样(RSS)是一种有效的方案,广泛用于产生更精确的估计器。尽管RSS很受欢迎,但它也有一些缺点,包括对异常值的高敏感性,有时不能适用于人口相对较少的情况。为了克服这些限制,最近引入了可变L秩集采样(VLRSS)。结果表明,VLRSS方案比RSS方案具有许多有趣的特性,并且涵盖了几种现有的RSS方案。此外,它还有助于提供若干总体参数的精确估计。为了填补这一空白,本文扩展了这方面的工作,解决了在强度和应力均服从指数分布的情况下,基于VLRSS的系数估计问题。考虑了极大似然法和贝叶斯法来估计。利用广义熵损失函数和LINEX损失函数下的伽马分布得到贝叶斯估计量。通过仿真研究和工业现场的真实数据集,对基于VLRSS的估计器的性能进行了研究。结果表明,在排序质量较好的情况下,所提出的估计器在L排序集抽样下比同类估计器效率更高。
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引用次数: 0
Working Vacation Policy for Load Sharing K-out-of-N: G System N:G系统中K-out-of-G负载共享的工作休假策略
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-09-30 DOI: 10.13052/jrss0974-8024.1528
Sudeep Kumar, Ritu Gupta
In industrial systems, the K-out-of-N: G system is a prominent type of redundancy. The load sharing protects such system from malfunctioning/destroying and avoids overload problem that affects the system reliability in a significant manner. In this paper we develop a Markovian model of load-sharing K-out-of-N: G system having non-identical repairable components wherein the server may on working vacation. During his vacation period, the server repairs the failed components with different service rates rather than completely terminating service rate. The failed component gets immediately repaired by the server if not on vacation, and unequal load is distributed among remaining surviving components. The lifetime of each component is load dependent followed by non-identical exponential distribution with different failure rates. The system is failed down due to common cause with failure density which is also exponentially distributed. We suggest closed structure analytic expressions for reliability, cost estimation and other performance measures of the load-sharing K-out-of-N: G repairable system by incorporating the concept of working vacation. For the solution aspiration, Runge-Kutta method is utilized to solve the system of differential equations. Furthermore, we perform the numerical analysis for two illustrations 1-out-of-3: G system and 3-out-of-4: G system. The numerical simulation is carried out for the validation of analytical results which are exhibited and compared by giving numerical outcomes and neuro-fuzzy outcomes based on fuzzy interference system with the help of MATLAB.
在工业系统中,k -out- n: G系统是一种突出的冗余类型。负载共享保护了这样的系统不发生故障/破坏,并在很大程度上避免了影响系统可靠性的过载问题。本文建立了具有非相同可修部件的负载共享k -out- n: G系统的马尔可夫模型,其中服务器可能处于工作休假状态。在休假期间,服务器以不同的服务速率修复故障组件,而不是完全终止服务速率。如果不在休假期间,故障组件将立即由服务器修复,并且在剩余的幸存组件之间分配不相等的负载。各部件的寿命与载荷有关,并且在不同的故障率下呈不同的指数分布。系统是由共同原因引起的故障,故障密度呈指数分布。通过引入工作假期的概念,提出了负荷共享k -out- n: G可修系统可靠性、成本估算和其他性能指标的封闭结构解析表达式。在求解过程中,采用龙格-库塔法求解微分方程组。此外,我们还对两种典型的1-out- 3: G系统和3-out- 4: G系统进行了数值分析。在MATLAB的帮助下,通过给出基于模糊干扰系统的数值结果和神经模糊结果,对所展示的分析结果进行了验证和比较。
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引用次数: 1
The Bayesian Reliability Analysis of the Alpha Power Gompertz Model Alpha幂Gompertz模型的贝叶斯可靠性分析
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-09-30 DOI: 10.13052/jrss0974-8024.1529
J. T. Eghwerido, Suraju Olaniyi Ogundele, L. Nzei, F. Agu
This article introduced the determination of reliability analysis of the alpha power Gompertz model using the Bayesian techniques. The method developed has been evaluated using women breast cancer in the Stan implementation in R. A survival data used illustrates the proposed Bayesian approach.
本文介绍了利用贝叶斯技术确定α-幂Gompertz模型的可靠性分析。在R的Stan实施中,使用女性乳腺癌症对所开发的方法进行了评估。所使用的生存数据说明了所提出的贝叶斯方法。
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引用次数: 0
Knowledge and Awareness of COVID-19 in Uttar Pradesh: An Exploratory Data Analysis 北方邦对新冠肺炎的认识和认识:探索性数据分析
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-08-03 DOI: 10.13052/jrss0974-8024.1526
Prayas Sharma, N. K. Adichwal, A. K. Singh
Corona viruses, commonly called COVID-19, are a large family of viruses that can cause diseases ranging from the common cold to Severe Acute Respiratory Syndrome (SARS). Worldwide Covid-19 is affecting 210 countries and territories around the world and two international conveyances. As of 2 June 2020, there are 6,408,869 confirmed 2,935,368 recovered and 378,317 deaths cases has been reported in world of Coronavirus diseases, India is not untouched from this situation. Currently, it has reported infected 190,535 and 5,394 death cases due to COVID-19 in India. (https://covid19.who.int/region/searo/country/in). The COVID-19 pandemic was first confirmed in the Indian state of Uttar Pradesh on 4 March 2020, with the first positive case in Ghaziabad. As of 1 June 2020, the state has 8361 confirmed cases, resulting in 222 deaths and 5030 recoveries. The situation is getting worst day by day as COVID-19 outbreaks and patients are increasing by every minute and become the most important issue for the whole world and So accessing knowledge and awareness among the people is very important. The present study using the exploratory data analysis we tried to demonstrate the knowledge and awareness of individuals about the COVID-19 pandemic in Uttar Pradesh, the most populous state of India. The findings of the present study can be utilized by the researchers and policy makers to handle this worst situation.
冠状病毒,通常被称为新冠肺炎,是一大类病毒,可导致从普通感冒到严重急性呼吸综合征(SARS)等疾病。新冠肺炎正在影响全球210个国家和地区以及两个国际运输工具。截至2020年6月2日,全球共有6408869例确诊病例、2935368例康复病例和378317例死亡病例,印度并非没有受到这种情况的影响。目前,印度已报告因新冠肺炎感染病例190535例,死亡病例5394例。(https://covid19.who.int/region/searo/country/in)。2020年3月4日,印度北方邦首次确诊新冠肺炎大流行,加齐阿巴德出现首例阳性病例。截至2020年6月1日,该州已有8361例确诊病例,导致222人死亡,5030人康复。随着新冠肺炎疫情的爆发和患者的每分钟增加,情况日益恶化,成为全世界最重要的问题,因此在人们中获得知识和认识非常重要。本研究使用探索性数据分析,试图证明印度人口最多的北方邦个人对新冠肺炎大流行的了解和认识。研究人员和政策制定者可以利用本研究的结果来应对这种最糟糕的情况。
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引用次数: 0
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Journal of Reliability and Statistical Studies
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