American Journal of Mathematical and Management Sciences

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. Shared frailty models are used despite their limitations. To overcome their disadvantages correlated frailty models may be used. In this paper, we introduce the correlated compound geometric frailty models with two different baseline distributions namely, the generalized log logistic and the generalized Weibull. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply these models to a real life bivariate survival data set of McGilchrist and Aisbett (Citation1991) related to the kidney infection data and a better model is suggested for the data.

David D. Hanagal

Analysis of Kidney Infection Data Using Correlated Compound Geometric Frailty Models

使用相关复合几何脆弱模型分析肾脏感染数据

G. Kannan

P. Jeyadurga

S. Balamurali

Economic Design of Generalized Multiple Dependent State Sampling Plan Under Exponentiated Half Logistic Distribution

指数化半逻辑分布下广义多重相关状态抽样计划的经济设计

Soft set theory has emerged recently as a new mathematical tool to handle uncertainty. Sometimes decision makers are not sure about the decision-making criteria, where soft set theory provides an idea to deal with such uncertainties. Multi-criteria decision making (MCDM) involves choosing the best from several alternatives. MCDM methods such as TOPSIS and VIKOR depend on an aggregating function for presenting “closeness to the ideal” which arises due to the compromise solution. The VIKOR method of compromise ranking describes a compromise solution, providing a maximum for the “maximizing player” and minimum for the “opponent”, which is an effective approach in an MCDM game. TOPSIS method presents a solution with the shortest distance to the positive ideal solution (PIS) and largest distance from the negative ideal solution (NIS). Also, hesitant fuzzy soft set is an appropriate tool to tackle the imprecise parameters introduced in MCDM problems by the decision maker (DM). In this paper, we extend the VIKOR and TOPSIS methods for solving MCDM game problems with hesitant fuzzy soft payoffs to determine the optimal strategies. Finally, a numerical example is incorporated to verify the extended VIKOR approach and the results are compared with those for the TOPSIS method. The paper ends with conclusions and outlooks.

Jishu Jana

Sankar Kumar Roy

Soft Matrix Game: A Hesitant Fuzzy MCDM Approach

软矩阵博弈：一种犹豫模糊多准则决策方法

During recent years, Last-mile deliveries (LMD) have become relevant due to its application in e-commerce, urban logistics, and food delivery among others. This work addresses an LMD denoted as a Vehicle Routing Problem with time windows (VRPTW) and aims to minimize total time of the distribution process (i.e., makespan). The LMD is an NP-Hard problem that refers to the delivery of goods from a consolidation center to a destination. For solving the problem, a spreadsheet-based solution that employs a multi-start algorithm based on the biased-randomized version of the nearest neighbor heuristic is introduced. Real historical data of last-mile deliveries for dairy products in Bogotá (Colombia) was considered for evaluating our proposed method. Computational experiments are carried out to show the competitiveness of our method in terms of makespan, number of vehicles, average vehicle occupancy, average load and costs. Some insights for future works are also provided.

José G. Sanabria-Rey

Elyn L. Solano-Charris

Carlos Alberto Vega-Mejía

Carlos L. Quintero-Araújo

Solving Last-Mile Deliveries for Dairy Products Using a Biased Randomization-Based Spreadsheet. A Case Study

基于偏随机化的电子表格解决乳制品最后一公里配送问题：案例研究

This paper introduces multi-sample Type-II progressive hybrid censoring which allows to incorporate data from k≥2 independently conducted Type-II (progressive) hybrid censored experiments for the first time. Assuming exponentially distributed lifetimes with mean ϑ, the maximum likelihood estimator of ϑ is obtained and its exact distribution is established. Moreover, we propose an exact confidence interval as well as two asymptotic confidence intervals for the unknown mean. The results are illustrated by simulations and a data set.

Marcel Jansen

Erhard Cramer

Julian Gorny

Exact Likelihood Inference for an Exponential Parameter under a Multi-Sample Type-II Progressive Hybrid Censoring Model

多样本II型逐步混合截尾模型下指数参数的精确似然推断

Proloy Banerjee

Shreya Bhunia

Baishampayan Seal

Partial Bayes Estimation in Two-Parameter Rayleigh Distribution

两参数瑞利分布中的部分贝叶斯估计

Dombi et al. introduced the omega distribution with three positive parameters and proved that its asymptotic distribution is the Weibull model. We propose the unit omega distribution with support in (0,1), and obtain a linear representation for its density function. The maximum likelihood and Bayesian methods are adopted for estimating the model parameters. It is conducted Monte Carlo simulations to examine the means, biases, and square roots of the mean square errors of the maximum likelihood estimators. The importance of the new distribution is proved by means of antimicrobial resistance data.

Fábio Prataviera

Gauss M. Cordeiro

The Unit Omega Distribution, Properties and Its Application

单位Omega分布，性质及其应用

A discrete version of the continuous half-logistic distribution is introduced, which is based on the minimization of the Cramér distance between the corresponding continuous and step-wise cumulative distribution functions. The expression of the probability mass function is derived in an analytic form, and some properties of the distribution - mainly related to moments and reliability concepts - are discussed. As for sample estimation, three different techniques are suggested, whose theoretical and empirical features are examined also through a Monte Carlo simulation study, comprising several parameter and sample size combinations. A comparison is also made between the proposed distribution and a discrete version already proposed in the literature, based on a different rationale, and a main difference is highlighted. A count regression model is suggested where the response variable follows the discrete half-logistic distribution and artificial and real data are used to illustrate its use. Finally, the performance of the proposed distribution over other classical models is discussed based on a real data set.

Alessandro Barbiero

Asmerilda Hitaj

An Alternative Discrete Analogue of the Half-Logistic Distribution Based on Minimization of a Distance between Cumulative Distribution Functions

基于累积分布函数间距离最小化的半逻辑分布的替代离散模拟

ISSN	0196-6324, 2325-8454
h-index	21

Publication Information	Publisher: Taylor and Francis Ltd.，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2013，Proportion of original research papers: 0.00%，Self Citation Rate:N.A.， Gold OA Rate: 0.00%

American Journal of Mathematical and Management Sciences

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Analysis of Kidney Infection Data Using Correlated Compound Geometric Frailty Models

Economic Design of Generalized Multiple Dependent State Sampling Plan Under Exponentiated Half Logistic Distribution

Soft Matrix Game: A Hesitant Fuzzy MCDM Approach

Solving Last-Mile Deliveries for Dairy Products Using a Biased Randomization-Based Spreadsheet. A Case Study

Exact Likelihood Inference for an Exponential Parameter under a Multi-Sample Type-II Progressive Hybrid Censoring Model

Analysis of Kidney Infection Data Using Correlated Compound Geometric Frailty Models

Economic Design of Generalized Multiple Dependent State Sampling Plan Under Exponentiated Half Logistic Distribution

Partial Bayes Estimation in Two-Parameter Rayleigh Distribution

The Unit Omega Distribution, Properties and Its Application

An Alternative Discrete Analogue of the Half-Logistic Distribution Based on Minimization of a Distance between Cumulative Distribution Functions