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Statistical Analysis of the Beta Transmuted Standardized Half Logistic Distribution: Properties, Estimation, and Real-Data Application β转化标准化半Logistic分布的统计分析:性质、估计和实际数据应用
Pub Date : 2023-10-25 DOI: 10.9734/ajpas/2023/v25i2554
P. O. Awodutire, E. C. Nduka, A. Olosunde
In this paper, a new distribution called the Beta Transmuted Half Logistic Distribution is derived and studied using the Beta Transmuted-G distribution. The distribution generalizes the half logistic distribution for more flexibility. Then expressions for the moments, moment generating function, order statistic, survival function, and the hazard function were studied. Estimation of parameters of the model was done using the maximum likelihood estimation approach. Simulation studies were conducted to assess the performance of the estimates of the parameter. Furthermore, the distribution is applied to a real-life dataset, demonstrating its superior performance in terms of producing a better fit compared to its submodels. This research contributes to the field of probability distributions and provides a valuable tool for modeling and analyzing various types of data.
本文利用Beta变形- g分布,推导并研究了一个新的Beta变形半Logistic分布。该配送推广了半物流配送,具有更大的灵活性。然后研究了矩、矩生成函数、阶统计量、生存函数和危险函数的表达式。采用极大似然估计方法对模型参数进行估计。进行了仿真研究,以评估参数估计的性能。此外,将该分布应用于实际数据集,与子模型相比,证明了其在产生更好的拟合方面的优越性能。该研究为概率分布领域做出了贡献,并为建模和分析各种类型的数据提供了有价值的工具。
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引用次数: 0
On Propositions Pertaining to the Riemann Hypothesis II 关于黎曼假设的命题2
Pub Date : 2023-10-14 DOI: 10.9734/ajpas/2023/v25i2553
Pathikrit Basu
Aims/Objectives: In this paper, we define certain classes of non-zeroes of the Riemann zeta function. We also present associated algorithms for finding these non-zeroes, which can enable corresponding computations. Some theoretical connections are also drawn with mixed integer programming and continuous Diophantine approximation. We also study, for points in the domain of the Riemann zeta function, their induced distributions over the unit circle.
目的:在本文中,我们定义了若干类黎曼ζ函数的非零。我们还提出了查找这些非零的相关算法,从而可以进行相应的计算。利用混合整数规划和连续丢番图近似,给出了一些理论联系。对于黎曼ζ函数域中的点,我们也研究了它们在单位圆上的诱导分布。
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引用次数: 0
Portfolio Optimization Using 0-1 Knapsack Quadratic Programming Model: A Case Study 基于0-1背包二次规划模型的投资组合优化:一个案例研究
Pub Date : 2023-10-14 DOI: 10.9734/ajpas/2023/v25i2552
Nneka O. Iheonu, Chiemena G. Ebirilem
Portfolio management is critical to selecting the right mix of investments which produces the best of results for any business entity. Using the 0-1 Knapsack quadratic model together with the mean-variance approach, this study sought to determine the optimal asset mix for TCF Microfinance bank. Five asset types were evaluated at a 70% target return. After three iterations, an optimal portfolio mix constituting of three out of the five assets was achieved, which exceeded the predetermined benchmark by 49.3% and at a risk value of less than 5%. This optimal investment can easily be practically applied.
投资组合管理对于选择正确的投资组合至关重要,这对任何业务实体都能产生最佳结果。本研究采用0-1背包二次模型结合均值-方差方法,试图确定TCF小额信贷银行的最优资产组合。五种资产类型以70%的目标回报率进行评估。经过三次迭代,获得了由5种资产中的3种构成的最优组合组合,超出预定基准49.3%,风险值小于5%。这种最优投资可以很容易地实际应用。
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引用次数: 0
Modelling Count Variables: A Comparative Analysis of two Discretization Techniques 计数变量建模:两种离散化技术的比较分析
Pub Date : 2023-10-11 DOI: 10.9734/ajpas/2023/v25i2551
J. A. Ademuyiwa, S. R. M. Sabri, A. A. Adetunji
Background: Different discretization methods have been proposed to provide a better fit to count observations with characteristics resembling a given continuous distribution. This is done to provide discrete distribution with characteristics resembling a chosen continuous distribution. This study compares discretization through survival function and mixed Poisson processes. Methodology: The Ailamujia distribution is extended using the cubic rank transmutation map. The shapes and some moment based properties of the continuous distribution are obtained. Two discretized versions of the distribution obtained are unimodal and skewed, depicting characteristics of the continuous distribution. Parameters of the new discrete distributions are estimated using the method of maximum likelihood, and both AIC and chi-square are used for model comparison. Results: Real-life assessment using five count data shows that the two propositions provide a better fit than the three competing distributions considered. Also, discretization through the mixed Poisson process offers a better fit than the survival function technique. Conclusion: Various moment-based mathematical properties of the discretization through the mixed Poisson process are easily obtainable and hence, can be easily characterized.
背景:人们提出了不同的离散化方法,以提供更好的拟合,以计算具有类似给定连续分布特征的观测值。这样做是为了使离散分布具有与选定的连续分布相似的特征。本研究比较了生存函数离散化和混合泊松过程离散化。 方法:利用三次秩变换图对艾拉木家分布进行扩展。得到了连续分布的形状和一些基于矩的性质。得到的分布的两个离散版本是单峰和偏态,描述了连续分布的特征。使用极大似然法估计新离散分布的参数,并使用AIC和卡方进行模型比较。 结果:使用五计数数据的实际评估表明,这两个命题比考虑的三个竞争分布提供了更好的拟合。此外,通过混合泊松过程离散化比生存函数技术提供了更好的拟合。 结论:通过混合泊松过程离散化的各种基于矩的数学性质很容易得到,因此可以很容易地表征。
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 Results: Real-life assessment using five count data shows that the two propositions provide a better fit than the three competing distributions considered. Also, discretization through the mixed Poisson process offers a better fit than the survival function technique.
 Conclusion: Various moment-based mathematical properties of the discretization through the mixed Poisson process are easily obtainable and hence, can be easily characterized.","PeriodicalId":8532,"journal":{"name":"Asian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136211018","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 of Eggenberger–Polya Distribution as an Alternative Model for Dry Spell Analysis in Northern Odisha, India 利用Eggenberger-Polya分布作为印度奥里萨邦北部干旱期分析的备选模型
Pub Date : 2023-10-07 DOI: 10.9734/ajpas/2023/v25i2550
Tapan Kumar Malik, A. K. Mangaraj, L. N. Sahoo
In this paper, Eggenberger–Polya distribution has been preferred as an alternative to a 2-state Markov Chain model for characterizing persistence behaviour of dry spell for Northern Odisha, India during south-west monsoon season. An attempt has been made to compare performance of the two competing models with reference to their strength to fit the empirical distribution of dry spell length under two goodness-of-fit criteria.
在本文中,Eggenberger-Polya分布被首选作为表征西南季风季节印度奥里萨邦北部干旱持续行为的2态马尔可夫链模型的替代。在两个拟合优度标准下,比较了两个相互竞争的模型在拟合干旱期长度的经验分布方面的表现。
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引用次数: 0
An Application of Homogenous Semi-Markov Model for Assessing HIV/AIDS Progression to ART Patients in Namibia 齐次半马尔可夫模型在评估纳米比亚抗逆转录病毒治疗患者艾滋病进展中的应用
Pub Date : 2023-10-06 DOI: 10.9734/ajpas/2023/v25i1547
Simon Pombili Kashihalwa, Josua Mwanyekange, Lilian Pazvakawambwa
Background: The progression of HIV infection to AIDS and then to death can be considered a stochastic process. Disease progression can be broken down into a finite number of intermediate states, based on CD4 counts. The five states of the Markov process of HIV/AIDS progression are commonly defined as: S1: CD4 count > 500 cells/microliter; S2: 350 < CD4 count ≤ 500 cells/microliter; S3: 200 < CD4 count ≤ 350 cells/microliter; S4: CD4 count ≤ 200 cells/microliter; and D: Death. Objectives: The objective of this study was to model the progression of HIV/AIDS disease of patients under ART follow-up in Namibia using homogenous semi-Markov processes, using the data obtained from Ministry of Health and Social Services. Methods: A retrospective study design was used to obtain data on 2422 patients who were observed 11028 times. The semi-Markov model was employed to estimate the transition probabilities and transition intensity rate. Time Homogeneous Semi-Markov model was fitted to assess effectiveness of ART by comparing the forward transition and reverse transitions. Results: As expected the probabilities of transiting from good states to worse states increased with time (from state 1 to state 3 and 4 after 6 months is 0.023 and 0.004, after 12 months is 0.059 and 0.010 respectively). As time increase the probabilities of remaining in the same state is decreasing (probabilities of remaining in state 1 after 6, 12 and 18 months is 0.804, 0.698 and 0.633). As expected the intensity indicates that the rate of transiting from good states to worst states is decreasing (the intensity of transiting from state 1 to 3 and 4 is p<0.001). The strongest predictor of transition from state 1 to 2 is TDF/3TC/EFV, which has a hazard ratio of 1.338 (with p value of 0.002). Patients who were prescribed TDF/3TC/EFV, are over 1.338 times more likely to transit from state 1 to state 2 than patients who did not receive TDF/3TC/EFV. A hazard ratio of 0.678 for the predictor variable female shows that female were less likely to transit from state 2 to 3 than their male counterparts. The hazard ratios of females from a bad state to a better state are more than 1, which is an indication that females are less likely to respond to treatment compared to males. Conclusions: HIV can progress to AIDS without delay if there is no intervention. Early ART initiation is crucial to reduce the probabilities of transiting from good states to worse states.
背景:从HIV感染到艾滋病再到死亡的进展可以被认为是一个随机过程。基于CD4计数,疾病进展可以被分解为有限数量的中间状态。HIV/AIDS进展马尔可夫过程的五种状态通常定义为:S1: CD4计数>500个细胞/微升;S2: 350 <CD4计数≤500个细胞/微升;S3: 200 <CD4计数≤350个/微升;S4: CD4计数≤200个细胞/微升;and D: Death. 目的:本研究的目的是利用从卫生和社会服务部获得的数据,利用同质半马尔可夫过程,对纳米比亚接受抗逆转录病毒治疗随访的患者的艾滋病毒/艾滋病疾病进展进行建模。方法:采用回顾性研究设计,收集2422例患者资料,共观察11028次。采用半马尔可夫模型估计过渡概率和过渡强度率。拟合时间齐次半马尔可夫模型,通过比较正向转换和反向转换来评估ART的有效性。 结果:正如预期的那样,从良好状态过渡到较差状态的概率随着时间的推移而增加(6个月后从状态1过渡到状态3和状态4的概率分别为0.023和0.004,12个月后分别为0.059和0.010)。随着时间的增加,处于同一状态的概率逐渐减小(6个月、12个月和18个月后处于状态1的概率分别为0.804、0.698和0.633)。正如预期的那样,强度表明从良好状态向最差状态过渡的速率正在降低(从状态1到状态3和状态4的过渡强度为p<0.001)。TDF/3TC/EFV是状态1向状态2过渡的最强预测因子,其风险比为1.338 (p值为0.002)。服用TDF/3TC/EFV的患者从状态1过渡到状态2的可能性是未服用TDF/3TC/EFV的患者的1.338倍。预测变量女性的风险比为0.678,表明女性比男性更不可能从状态2过渡到状态3。女性从不良状态到较好状态的风险比大于1,这表明与男性相比,女性对治疗的反应较小。 结论:如果不采取干预措施,HIV可迅速发展为艾滋病。早期开始抗逆转录病毒治疗对于减少从良好状态过渡到较差状态的可能性至关重要。
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引用次数: 0
Measuring and Evaluating the Services of Kumasi Technical University Restaurant by Employing Statistical Process Control Tools 运用统计过程控制工具对库马西技术大学餐厅服务进行测量与评价
Pub Date : 2023-10-06 DOI: 10.9734/ajpas/2023/v25i2548
Mary Ann Yeboah, Francis Yao Anyan, Rosemary Abayase
The study measures and evaluates Kumasi Technical University (KsTU) Restaurant’s services using statistical process control tools. Two categories of respondents (members of staff and students) were engaged in the study. Data was collected from 100 members of staff and 223 students using questionnaires. Statistical tools such as mean, pareto charts and factor analysis were used in the analysis. The results shows that respondents are highly satisfied with the services provided by the restaurant. The survey also found that consumers consider two factors, namely atmosphere and food quality, while evaluating the services offered by a restaurant.
本研究使用统计过程控制工具测量和评估库马西技术大学(KsTU)餐厅的服务。两类受访者(教职员工和学生)参与了这项研究。数据是通过问卷调查从100名教职员工和223名学生中收集的。采用均值、帕累托图、因子分析等统计工具进行分析。结果显示,受访者对餐厅提供的服务非常满意。调查还发现,消费者在评价一家餐厅提供的服务时,会考虑两个因素,即氛围和食物质量。
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引用次数: 0
A Bayesian Nonparametric Modeling Approach to Settlement Patterns of Pastoralists Population in Kenya 肯尼亚游牧人口定居模式的贝叶斯非参数建模方法
Pub Date : 2023-10-06 DOI: 10.9734/ajpas/2023/v25i2549
Amos Kipkorir Langat, Michael Arthur Ofori, Mouhamadou Djima Baranon, Daniel Bekalo Biftu, Samuel Musili Mwalili
Pastoralists' settlement patterns in Kenya have been studied for decades using various statistical and mathematical models. However, traditional models have often relied on restrictive assumptions, such as the normality of the data or the linearity of relationships. In this paper, we apply a Bayesian nonparametric approach to model the settlement patterns of pastoralists in Kenya, allowing for more flexible and realistic representations of the data. We first collected settlement data for pastoralists in Kenya and compiled a database of environmental covariates, such as distance to water sources, vegetation cover, and road networks. We then applied a Bayesian nonparametric clustering method to identify distinct settlement patterns and tested the performance of the model against other commonly used clustering techniques. Our results indicate that the Bayesian nonparametric approach outperforms other clustering techniques in terms of model fit and accuracy in identifying distinct settlement patterns. Additionally, we conducted a spatial regression analysis to investigate the relationship between settlement patterns and environmental covariates, revealing that distance to water sources and road networks are significant predictors of settlement patterns. Overall, our study highlights the usefulness of Bayesian nonparametric methods in modelling settlement patterns of pastoralists in Kenya and provides valuable insights into the relationship between environmental factors and settlement patterns.
几十年来,人们一直在使用各种统计和数学模型研究肯尼亚牧民的定居模式。然而,传统模型往往依赖于限制性假设,例如数据的正态性或关系的线性。在本文中,我们应用贝叶斯非参数方法来模拟肯尼亚牧民的定居模式,允许更灵活和现实的数据表示。我们首先收集了肯尼亚牧民的定居数据,并编制了一个环境协变量数据库,如到水源的距离、植被覆盖和道路网络。然后,我们应用贝叶斯非参数聚类方法来识别不同的沉降模式,并测试了该模型与其他常用聚类技术的性能。我们的研究结果表明,贝叶斯非参数方法在模型拟合和识别不同聚落模式的准确性方面优于其他聚类技术。此外,我们通过空间回归分析探讨了聚落模式与环境协变量之间的关系,发现到水源的距离和道路网络是聚落模式的重要预测因子。总的来说,我们的研究强调了贝叶斯非参数方法在肯尼亚牧民定居模式建模中的实用性,并为环境因素与定居模式之间的关系提供了有价值的见解。
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引用次数: 0
Determinants of Institutional Delivery in Bangladesh: A Multilevel Analysis of a Nationwide Population-Based Survey 孟加拉国制度交付的决定因素:一项基于全国人口调查的多层次分析
Pub Date : 2023-10-05 DOI: 10.9734/ajpas/2023/v25i1546
Shahjadi Ireen, Most Sifat Muntaha Soni, Muhammad Tareq, Md. Zahid Hasan, Salma Akter, Shahanaj Parvin, Rebeka Sultana, Mansura Begum, Md. Matiur Rahman Molla
Background: A substantial number of mothers and infants lose their lives due to complications during childbirth. Institutional delivery can lower the number of fatalities. This study aims to explore the prevalence of institutional delivery and its multifaceted associated factors in Bangladesh. Methods: The data were extracted from Bangladesh Demographic and Health Survey (BDHS), conducted during the period of 2017-18. Following data preprocessing, a total of 4974 women were included in this study. This study attempts to identify and assess the variables (at the individual and community levels) having the significant impact on the institutional delivery by using a multilevel binary logistic regression model. Results: Approximately half of the Bangladeshi women's deliveries were done at the medical center. The study found that women aged 20 or older had a 1.53 times greater likelihood of using healthcare facilities during childbirth (OR 1.53, [1.31-1.78]) than those under 20. Women with higher levels of education were more than twice as likely to choose institutional delivery as those with no education, and the women whose husbands had higher education had the same likelihood. The likelihood of using an institutional delivery service was also boosted by women's higher socioeconomic status. Women with exposure to any form of media had a 36% (OR 1.36, [1.16-1.60] higher likelihood of accessing healthcare facilities during childbirth. Rural women had a 20% lower likelihood of receiving institutional delivery. The utilization of institutional delivery was positively correlated with religion, geographical region, child ever born, and antenatal care visits (ANC). This study discovered significant variations at the community level. Conclusion: In order to increase the prevalence of institutional delivery in Bangladesh, the study findings suggest that policymakers should focus on addressing socioeconomic and demographic factors, particularly on women's education, husbands' education, age at first delivery and frequency of ANC visits.
背景:大量的母亲和婴儿因分娩并发症而失去生命。机构提供服务可以降低死亡人数。本研究旨在探讨机构交付在孟加拉国的普遍性及其多方面的相关因素。 方法:数据提取自2017-18年孟加拉国人口与健康调查(BDHS)。经数据预处理,本研究共纳入4974名女性。本研究试图通过使用多层次二元logistic回归模型来识别和评估对机构交付产生重大影响的变量(在个人和社区层面)。 结果:大约一半的孟加拉国妇女在医疗中心分娩。研究发现,20岁及以上的女性在分娩期间使用医疗设施的可能性是20岁以下女性的1.53倍(or 1.53,[1.31-1.78])。受教育程度较高的妇女选择机构分娩的可能性是未受教育妇女的两倍多,丈夫受过高等教育的妇女选择机构分娩的可能性也相同。妇女较高的社会经济地位也提高了使用机构分娩服务的可能性。接触任何形式媒体的妇女在分娩期间获得医疗保健设施的可能性高出36% (OR 1.36,[1.16-1.60])。农村妇女接受机构分娩的可能性要低20%。机构分娩的利用与宗教、地理区域、出生儿童和产前保健访问(ANC)呈正相关。这项研究发现,在社区水平上存在显著差异。 结论:为了提高孟加拉国机构分娩的普及程度,研究结果表明,政策制定者应关注社会经济和人口因素,特别是妇女的教育程度、丈夫的教育程度、首次分娩年龄和ANC就诊频率。
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引用次数: 0
Prediction and Assessment of Stream Water Quality by Considering Multiple Water Quality Parameters 考虑多水质参数的河流水质预测与评价
Pub Date : 2023-10-02 DOI: 10.9734/ajpas/2023/v25i1544
None Senarathne S. G. J., None Thilan A. W. L. P.
Geostatistical studies entail identifying the most appropriate model to describe the observed data so that it can be used to accurately predict responses across a range of possible locations. The purpose of such a model is to depict the link between the response variables and the predictors while taking into account uncertainties in space and time. We propose a novel approach to model such data via a multivariate spatio-temporal additive model derived through considering a multivariate normal approximation. To demonstrate how the proposed approach works, we use numerous water quality parameters to model and predict the water quality of a stream network. To re ect the spatial variability of the stream network, we employed hydrologic distances in the model, which allowed certain properties of streams and rivers, such as stream ow connectivity, to be effectively described. It was observed that the proposed multivariate model produces accurate predictions at un-sampled locations compared to its univariate counterparts. Accordingly, this study reveals that the proposed multivariate modelling approach is a viable alternative for modelling complicated data such as the data found in water quality monitoring.
地质统计研究需要确定最合适的模型来描述观测到的数据,以便它可以用来准确预测一系列可能位置的反应。这种模型的目的是在考虑到空间和时间上的不确定性的情况下,描述响应变量和预测因子之间的联系。我们提出了一种新的方法,通过考虑多元正态近似推导出的多元时空加性模型来建模这些数据。为了证明所提出的方法是如何工作的,我们使用了许多水质参数来建模和预测河流网络的水质。为了反映河流网络的空间变异性,我们在模型中采用了水文距离,这使得溪流和河流的某些特性,如水流连通性,能够被有效地描述。观察到,与单变量模型相比,所提出的多变量模型在未采样位置产生准确的预测。因此,本研究表明,所提出的多变量建模方法是对复杂数据(如水质监测数据)建模的可行替代方法。
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引用次数: 0
期刊
Asian Journal of Probability and Statistics
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