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Mixture of Birnbaum-Saunders Distributions: Identifiability, Estimation and Testing Homogeneity with Randomly Censored Data Birnbaum-Saunders分布的混合：随机截尾数据的可识别性、估计和检验齐性
American Journal of Mathematical and Management Sciences Pub Date : 2020-10-24 DOI: 10.1080/01966324.2020.1837041
Walaa A. El-Sharkawy, M. Ismail
{"title":"Mixture of Birnbaum-Saunders Distributions: Identifiability, Estimation and Testing Homogeneity with Randomly Censored Data","authors":"Walaa A. El-Sharkawy, M. Ismail","doi":"10.1080/01966324.2020.1837041","DOIUrl":"https://doi.org/10.1080/01966324.2020.1837041","url":null,"abstract":"Abstract Random censoring is frequently utilized to analyze lifetime data in life-testing and reliability experiments. However, no published work discussed parameter estimation and testing homogeneity under random censoring for the mixture of Birnbaum-Saunders (BS) distributions, which is a useful model for describing reliability data. In this paper, first the proof of the identifiability of a finite mixture of BS distributions with g components is developed using Laplace transform of BS distributions. Then based on random censoring, parameter estimation and testing homogeneity are discussed. An EM algorithm is proposed to obtain the maximum likelihood (ML) estimates of the mixture model parameters and an EM test is implemented to test for homogeneity in the mixture of BS distributions. A Monte Carlo simulation study is conducted to evaluate the performance of the ML estimates through the bias and mean squared error. Additionally, the performance of the EM test is investigated through its size and power which are calculated by Monte Carlo simulation. Finally, an example of aircraft Windshield data is used to illustrate the estimation and testing procedures.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"225 - 240"},"PeriodicalIF":0.0,"publicationDate":"2020-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1837041","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49403579","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: 2
Bounded Weighted Exponential Distribution with Applications 有界加权指数分布及其应用
American Journal of Mathematical and Management Sciences Pub Date : 2020-10-20 DOI: 10.1080/01966324.2020.1834893
Avishek Mallick, I. Ghosh, S. Dey, D. Kumar
{"title":"Bounded Weighted Exponential Distribution with Applications","authors":"Avishek Mallick, I. Ghosh, S. Dey, D. Kumar","doi":"10.1080/01966324.2020.1834893","DOIUrl":"https://doi.org/10.1080/01966324.2020.1834893","url":null,"abstract":"Abstract In this article, we try to supplement the distribution theory literature by incorporating a new bounded distribution, called the bounded weighted exponential (BWE) distribution in the (0, 1) intervals by transformation method. The proposed distribution exhibits decreasing and left-skewed unimodal density while the hazard rate can have increasing and bathtub shaped. Although our main focus is on the estimation from the frequentist point of view, in addition, we derive some useful structural and statistical properties of the proposed BWE distribution. We briefly describe three classical estimators namely, the maximum likelihood estimators (MLE), the ordinary least-squares estimators (LSE) and the weighted least-squares estimators (WLSE). Monte Carlo simulations are performed to compare performances of the proposed methods of estimation for both moderate and large samples. An application of the model is presented by re-analyzing a real data set and comparisons are made with the fit attained by some other well-known distributions for illustrative purposes.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"68 - 87"},"PeriodicalIF":0.0,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1834893","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45169865","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: 3
Evaluating the Project Completion Time When Non-Identical Beta Distributions Govern the Activity Networks 当非相同贝塔分布控制活动网络时评估项目完成时间
American Journal of Mathematical and Management Sciences Pub Date : 2020-08-28 DOI: 10.1080/01966324.2020.1812015
H. M. Barakat, Y. H. Abdelkader, T. Taher
{"title":"Evaluating the Project Completion Time When Non-Identical Beta Distributions Govern the Activity Networks","authors":"H. M. Barakat, Y. H. Abdelkader, T. Taher","doi":"10.1080/01966324.2020.1812015","DOIUrl":"https://doi.org/10.1080/01966324.2020.1812015","url":null,"abstract":"Abstract The main purpose of this paper is to determine the project completion time using a recursive method, where the activity times are distributed according to a sequence of beta distributions with unequal location parameters. For this purpose, we first evaluate the kth moment of the maximum of independent random variables that follow this sequence of distributions. Some illustrative examples are presented to demonstrate the applicability and appropriateness of this generalized beta model. These examples show that, the suggested estimate of project completion time is situated between the lower bound estimate (PERT) and the upper estimate that was obtained by Kambarowski. Moreover, this estimate has lowest variance among the other known estimates. Comparisons with other exemplary estimates (e.g., exponential, Erlang and Weibull estimates), discussed in literature, are presented.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"32 - 43"},"PeriodicalIF":0.0,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1812015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45706453","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: 3
A Noble Genetic Algorithm to Solve a Solid Green Traveling Purchaser Problem with Uncertain Cost Parameters 求解成本参数不确定的固体绿色旅行购买者问题的贵族遗传算法
American Journal of Mathematical and Management Sciences Pub Date : 2020-08-21 DOI: 10.1080/01966324.2020.1805060
Arindam Roy, Rong Gao, Lifen Jia, Samir Maity, S. Kar
{"title":"A Noble Genetic Algorithm to Solve a Solid Green Traveling Purchaser Problem with Uncertain Cost Parameters","authors":"Arindam Roy, Rong Gao, Lifen Jia, Samir Maity, S. Kar","doi":"10.1080/01966324.2020.1805060","DOIUrl":"https://doi.org/10.1080/01966324.2020.1805060","url":null,"abstract":"Abstract The traveling purchaser problem (TPP) is a notable generalization of the traveling salesman problem (TSP) which involves selecting a subset of markets at a minimum traveling cost such that the demand for each product is satisfied. A solid green traveling purchaser problem (SGTPP) is a TPP in which, at each market, some conveyances are available to travel to another market with minimum cost considering the environmental impact caused by carbon emission. In this paper, we formulate an SGTPP with travel cost between each pair of markets and purchase price of the products as uncertain variables. Using uncertainty theory, an expected value model is formulated and then transformed into the corresponding deterministic form. Finally, a noble genetic algorithm (nGA) is designed to solve the proposed model. The algorithm is called noble because it adopts a crossover of the combination of a probabilistic selection of three parents, according to real-life In Vitro Fertilization (IVF) techniques. Computational results reveal that our proposal is favorably compared to previous algorithms in the existing literature.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"17 - 31"},"PeriodicalIF":0.0,"publicationDate":"2020-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1805060","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44811347","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: 7
Maximum Likelihood Estimators in Growth Curve Model with Monotone Missing Data 单调缺失数据生长曲线模型的极大似然估计
American Journal of Mathematical and Management Sciences Pub Date : 2020-08-03 DOI: 10.1080/01966324.2020.1791290
Ayaka Yagi, T. Seo, Y. Fujikoshi
{"title":"Maximum Likelihood Estimators in Growth Curve Model with Monotone Missing Data","authors":"Ayaka Yagi, T. Seo, Y. Fujikoshi","doi":"10.1080/01966324.2020.1791290","DOIUrl":"https://doi.org/10.1080/01966324.2020.1791290","url":null,"abstract":"Abstract This article focuses on the maximum likelihood estimators (MLEs) of the mean parameter vector and the covariance matrix in a one-sample version of the growth curve model when the dataset has a monotone missing pattern. First, a closed form is obtained for the MLE of the mean parameter vector when the covariance matrix is known. Similarly, it is obtained for the MLE of the covariance matrix when the mean parameter vector is known. The distributions of these estimators and their basic properties are also given. Then, considering that these expressions give the likelihood or determining equations, we propose an algorithm that includes an iterative procedure to obtain the MLEs when all the parameters are unknown. Further, a conventional estimator for the mean parameter vector is also proposed. Finally, a numerical example is given to illustrate our estimation procedure.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"1 - 16"},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1791290","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47708785","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
Tests and Confidence Intervals for the Mean of a Zero-Inflated Poisson Distribution 零膨胀泊松分布均值的检验和置信区间
American Journal of Mathematical and Management Sciences Pub Date : 2020-06-22 DOI: 10.1080/01966324.2020.1777914
Dustin Waguespack, K. Krishnamoorthy, Meesook Lee
{"title":"Tests and Confidence Intervals for the Mean of a Zero-Inflated Poisson Distribution","authors":"Dustin Waguespack, K. Krishnamoorthy, Meesook Lee","doi":"10.1080/01966324.2020.1777914","DOIUrl":"https://doi.org/10.1080/01966324.2020.1777914","url":null,"abstract":"Abstract The zero-inflated Poisson (ZIP) model is often postulated for count data that include excessive zeros. This ZIP distribution can be regarded as the mixture of two distributions, one that degenerate at zero and another is Poisson. Unlike the Poisson mean, the mean of the ZIP distribution is product of the mixture parameter and the Poisson parameter, and is not simple to make inference on the ZIP mean. In this article, the problem of making inference on the mean of a ZIP distribution is addressed. Confidence intervals based on the likelihood approach and bootstrap approach are provided. Signed likelihood ratio test for one-sided hypothesis is also developed. Proposed methods are evaluated for their properties by Monte Carlo simulation. Methods are illustrated using two examples.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"39 1","pages":"383 - 390"},"PeriodicalIF":0.0,"publicationDate":"2020-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1777914","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46774529","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: 5
Stationary Analysis of an Infinite-Buffer D-MAP/D-MSP/1 Queueing System 无限缓冲区D-MAP/D-MSP/1排队系统的平稳性分析
American Journal of Mathematical and Management Sciences Pub Date : 2020-06-16 DOI: 10.1080/01966324.2020.1777913
R. Nandi, S. K. Samanta
{"title":"Stationary Analysis of an Infinite-Buffer D-MAP/D-MSP/1 Queueing System","authors":"R. Nandi, S. K. Samanta","doi":"10.1080/01966324.2020.1777913","DOIUrl":"https://doi.org/10.1080/01966324.2020.1777913","url":null,"abstract":"Abstract This paper deals with the analysis of an infinite-buffer single-server D-MAP/D-MSP/1 queueing system. This queueing system can be analyzed by representing level-independent quasi-birth-and-death process in tridiagonal structure. The proposed analysis is based on the use of matrix-geometric method in conjunction with the spectral method to obtain the system-length distribution at outside observer’s epoch. We derive the stationary system-length distributions at random, prearrival, intermediate and post-departure epochs using the system-length distribution at outside observer’s epoch. The waiting-time distribution in the queue measured in slots of an arriving customer is also carried out. Computational procedures along with numerical results are provided to confirm the correctness of our analytical results.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"39 1","pages":"362 - 382"},"PeriodicalIF":0.0,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1777913","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41962061","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
Economic Return Quantity Model for a Multi-type Empty Container Management with Possible Storage Constraint and Shared Cost of Shipping 具有可能存储约束和分担运输成本的多类型空箱管理的经济退货量模型
American Journal of Mathematical and Management Sciences Pub Date : 2020-06-01 DOI: 10.1080/01966324.2020.1769516
O. Adetunji, S. Yadavalli, Rafid Alrikabi, Sebatjane Makoena
{"title":"Economic Return Quantity Model for a Multi-type Empty Container Management with Possible Storage Constraint and Shared Cost of Shipping","authors":"O. Adetunji, S. Yadavalli, Rafid Alrikabi, Sebatjane Makoena","doi":"10.1080/01966324.2020.1769516","DOIUrl":"https://doi.org/10.1080/01966324.2020.1769516","url":null,"abstract":"Abstract Containerization has been said to be one of the most significant innovations of port management in the last century. Some ports usually tend to be more export driven while some others are import driven. This imbalance in the number of inbound and outbound containers necessitates movement of containers from locations or surplus to those of deficit. A port needs to cater for not only the level of containers required, but also the variety. Many factors affect the cost efficiency of container movement, and hence, that of port operations, and these need to be managed in an integrated manner to optimize cost in a port. We studied the management of a multi-type container system in a port where there can be savings from joint movement of containers, both for empty return and for procurement of replacement containers, and where there is limited storage capacity. We developed a model to determine the optimal integrated return and purchase cycle times and quantities. We illustrated the solution approach with a numerical example and performed sensitivity analysis. We believe this problem is rife and the model can guide the management of container return and replenishment in ports operations.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"39 1","pages":"345 - 361"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1769516","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49078137","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: 3
Pivotal Inference for the Inverted Exponentiated Rayleigh Distribution Based on Progressive Type-II Censored Data 基于渐进II型截尾数据的逆指数瑞利分布的关键推断
American Journal of Mathematical and Management Sciences Pub Date : 2020-05-14 DOI: 10.1080/01966324.2020.1762142
Shuo Gao, Jiao Yu, Wenhao Gui
{"title":"Pivotal Inference for the Inverted Exponentiated Rayleigh Distribution Based on Progressive Type-II Censored Data","authors":"Shuo Gao, Jiao Yu, Wenhao Gui","doi":"10.1080/01966324.2020.1762142","DOIUrl":"https://doi.org/10.1080/01966324.2020.1762142","url":null,"abstract":"Abstract In this article, the pivotal inference is proposed to estimate the two unknown parameters of the inverse exponentiated Rayleigh distribution based on progressive censored data. We derive the point estimator and construct an interval estimator using the pivotal quantity method. To compare the performance of this proposed method and the traditional maximum likelihood estimation method, a simulation study is conducted. The simulation results show that the proposed method performs better in terms of bias and mean squared error. Finally, a real dataset is used to illustrate the proposed approaches.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"39 1","pages":"315 - 328"},"PeriodicalIF":0.0,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1762142","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49640766","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: 8
Ageing Intensity Function for Conditionally Specified Models 条件指定模型的老化强度函数
American Journal of Mathematical and Management Sciences Pub Date : 2020-05-13 DOI: 10.1080/01966324.2020.1762143
S. Sunoj, N. Nair, A. K. Nanda, R. Rasin
{"title":"Ageing Intensity Function for Conditionally Specified Models","authors":"S. Sunoj, N. Nair, A. K. Nanda, R. Rasin","doi":"10.1080/01966324.2020.1762143","DOIUrl":"https://doi.org/10.1080/01966324.2020.1762143","url":null,"abstract":"Abstract Jiang et al. have introduced a quantitative measure known as the ageing intensity function for evaluating the ageing properties of a component/system. The present study extends this ageing intensity function to the conditionally specified and conditional survival models. In a two component system, these two conditional ageing intensity functions provide the ageing patterns of one component when the other component has either failed or survived a specified period of time. The proposed conditionally ageing intensity function models provide simple expressions for some commonly used bivariate lifetime models. Characterization relationships are established for bivariate exponential, bivariate Weibull, conditional proportional hazards and bivariate weighted models.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"39 1","pages":"329 - 344"},"PeriodicalIF":0.0,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1762143","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44165929","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
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