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On a Modified Yule Distribution 修改后的圣诞分发
IF 1.9 Pub Date : 2018-10-02 DOI: 10.6092/ISSN.1973-2201/7990
C. Kumar, S. Harisankar
A modified version of Yule distribution is introduced here and discuss some of its properties by deriving expressions for its probability generating function, raw moments, factorial moments etc. Certain recursion formulae for its probabilities, raw moments and factorial moments are also developed. Various methods of estimation are employed for estimating the parameters of the distribution and certain test procedures are suggested for testing the significance of the additional parameters of the distribution. The distribution has been fitted to certain real-life data sets for illustrating its usefulness, compared with certain existing models available in the literature. Further, a simulation study is conducted for assessing the performance of the maximum likelihood estimators.
本文介绍了Yule分布的一个修正版本,并通过推导其概率生成函数、原始矩、阶乘矩等的表达式讨论了它的一些性质。还推导了它的概率、原始矩和阶乘矩的一些递推公式。采用各种估计方法来估计分布的参数,并建议采用某些测试程序来测试分布的附加参数的重要性。与文献中现有的某些模型相比,该分布已被拟合到某些现实生活中的数据集,以说明其有用性。此外,还进行了模拟研究,以评估最大似然估计器的性能。
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引用次数: 5
Quantile Approach of Dynamic Generalized Entropy (Divergence) Measure 动态广义熵(散度)测度的分位数方法
IF 1.9 Pub Date : 2018-10-02 DOI: 10.6092/ISSN.1973-2201/7201
Vikas Kumar, Rekha Rani
In the present paper, we propose a quantile version of generalized entropy measure for residual and past lifetimes and study their properties. Lower and upper bounds of the proposed measures are derived. Some of the quantile lifetime distributions have been characterized. We also introduce quantile versions of the generalized divergence measure of Varma between two residual and two past lifetime random variables. Some properties of this measure are studied and a characterization of the proportional (reversed) hazards model is given.
在本文中,我们提出了剩余寿命和过去寿命的广义熵测度的分位数版本,并研究了它们的性质。导出了所提出措施的下限和上限。已经对一些分位数寿命分布进行了表征。我们还引入了Varma在两个残差和两个过去寿命随机变量之间的广义散度测度的分位数版本。研究了该测度的一些性质,并给出了比例(反向)危险模型的特征。
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引用次数: 8
A New Family of Distributions Based on the Hypoexponential Distribution with Fitting Reliability Data 基于次指数分布的一类新分布及其可靠性数据拟合
IF 1.9 Pub Date : 2018-10-02 DOI: 10.6092/ISSN.1973-2201/8260
C. Chesneau
In this paper, a new general family of distributions using the hypoexponential distribution is introduced and studied. A special case of this family is explored in detail, corresponding to a new finite generalized mixture of generalized exponential distributions. Some of their mathematical properties are provided. We investigate maximum likelihood estimation of the model parameters. Two real data sets are used to prove the potential of this distribution among some recent extensions of the exponential distribution.
本文引入并研究了一个利用次指数分布的新的一般分布族。详细探讨了该族的一个特例,对应于广义指数分布的一个新的有限广义混合。提供了它们的一些数学性质。我们研究了模型参数的最大似然估计。在指数分布的一些最近的扩展中,使用两个真实数据集来证明这种分布的潜力。
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引用次数: 1
Methods of Estimating the Parameters of the Quasi Lindley Distribution 拟林德利分布参数的估计方法
IF 1.9 Pub Date : 2018-10-02 DOI: 10.6092/ISSN.1973-2201/8170
F. Opone, N. Ekhosuehi
In this paper, we review the quasi Lindley distribution and established its quantile function. A simulation study is conducted to examine the bias and mean square error of the parameter estimates of the distribution through the method of moment estimation and the maximum likelihood estimation. Result obtained shows that the method of maximum likelihood is a better choice of estimation method for the parameters of the quasi Lindley distribution. Finally, an applicability of the quasi Lindley disttribution to a waiting time data set suggests that the distribution demonstrates superiority over the power Lindley distribution, Sushila distribution and the classical oneparameter Lindley distribution in terms of the maximized loglikelihood, the Akaike information criterion, the Kolmogorov-Smirnov and Cramer von Mises test statistic.
本文综述了拟林德利分布,并建立了其分位数函数。通过矩估计法和极大似然估计法对分布参数估计的偏差和均方误差进行了仿真研究。结果表明,极大似然法是拟林德利分布参数估计的较好选择。最后,拟林德利分布对等待时间数据集的适用性表明,该分布在最大对数似然、Akaike信息准则、Kolmogorov-Smirnov和Cramer von Mises检验统计量方面优于幂林德利分布、Sushila分布和经典单参数林德利分布。
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引用次数: 1
Estimation of P(X>Y) for the Positive Exponential Family of Distributions 正指数分布族P(X>Y)的估计
IF 1.9 Pub Date : 2018-10-02 DOI: 10.6092/ISSN.1973-2201/7249
Ajit Chaturvedi, Ananya Malhotra
A positive exponential family of distributions is taken into consideration. Two measures of reliability are discussed. Uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are developed for the reliability functions. In addition to the UMVUES and MLES, we derive the method of moment estimators (MOME). The performances of two types of estimators are compared through Monte Carlo simulation.
考虑了一个正指数分布族。讨论了可靠性的两个度量标准。建立了可靠度函数的一致最小方差无偏估计量(UMVUES)和最大似然估计量(MLES)。除了UMVUES和MLES之外,我们还推导了矩估计量(MOME)的方法。通过蒙特卡罗模拟比较了两种估计量的性能。
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引用次数: 2
Statistical Inference for the Reliability Functions of a Family of Lifetime Distributions based on Progressive Type II Right Censoring 基于渐进式ⅱ型右截法的寿命分布族可靠性函数的统计推断
IF 1.9 Pub Date : 2018-07-12 DOI: 10.6092/ISSN.1973-2201/7494
Ajit Chaturvedi, Narendra Kumar, Kapil Kumar
In this article, a general family of lifetime distributions is considered under progressive type II right censoring. The classical point estimation and testing procedures are developed for reliability function and stress-strength reliability. The uniformly minimum variance unbiased, maximum likelihood and invariantly optimal estimators are considered. Testing procedures are developed for the hypotheses related to scale parameter, reliability and stress-strength reliability functions. A Monte Carlo simulation study is performed for comparison of various estimators developed. Finally, the use of proposed estimators is shown in an illustrative example.
在本文中,考虑了一个在渐进II型右删失下的寿命分布的一般族。建立了可靠性函数和应力强度可靠性的经典点估计和测试程序。考虑了一致最小方差无偏估计、最大似然估计和不变最优估计。针对与标度参数、可靠性和应力强度可靠性函数相关的假设,制定了测试程序。为了比较所开发的各种估计量,进行了蒙特卡罗模拟研究。最后,在一个示例中展示了所提出的估计量的使用。
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引用次数: 10
Induced Ranked Set Sampling when Units are Inducted from Several Populations 从多个种群中引入单位时的诱导排序集抽样
IF 1.9 Pub Date : 2018-07-12 DOI: 10.6092/ISSN.1973-2201/7187
P. Y. Thomas, A. Philip
The method of ranked set sampling when units are to be inducted from several bivariate populations is introduced in this work. The best linear unbiased estimation of a common parameter of two bivariate Pareto distributions is discussed based on the n ranked set observations, when a sample of size n 1 is drawn from a bivariate Pareto population with shape parameter a 1 and a sample of size n 2 is drawn from another bivariate Pareto with shape parameter a 2 such that n = n 1 + n 2 . The application of the results of this paper is illustrated with a real life data.
本文介绍了从多个二元总体中引入单元的排序集抽样方法。当从一个形状参数为a 1的二元Pareto总体中抽取一个大小为n 1的样本,并从另一个形状参数为a 2的二元Pareto总体中抽取一个大小为n 2的样本,使得n = n 1 + n 2时,讨论了基于n个排序集观测值的两个二元Pareto分布的一个公共参数的最佳线性无偏估计。并以实际数据说明了本文结果的应用。
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引用次数: 0
A Counting Process with Generalized Exponential Inter-Arrival Times 具有广义指数间隔到达时间的计数过程
IF 1.9 Pub Date : 2018-07-12 DOI: 10.6092/ISSN.1973-2201/7818
Sahana Bhattacharjee
This paper introduces a new counting process which is based on Generalized Exponentially distributed inter-arrival times. The advantage of this new count model over the existing Poisson count model is that the hazard function of the inter arrival time distribution is non-constant, so that the distribution is duration dependent and hence, is able to model both under dispersed and over dispersed count data, as opposed to the exponentially distributed inter arrival time of the Poisson count model, which is not duration dependent and the corresponding count model is able to model only equidispersed data. Further, some properties of this model are explored. Simulation from this new model is performed to study the behavior of count probabilities, mean and variance of the model for different values of the parameter. Use of the proposed model is illustrated with the help of real life data sets on arrival times of patients at a clinic and on arrival times of customers at a departmental store.
本文介绍了一种基于广义指数分布到达间隔时间的计数方法。与现有泊松计数模型相比,这种新的计数模型的优势在于,到达间时间分布的危害函数是非常数的,因此分布依赖于持续时间,因此能够模拟分散和过分散的计数数据,而泊松计数模型的指数分布到达间时间不依赖于持续时间,相应的计数模型只能模拟等分散的数据。进一步探讨了该模型的一些性质。利用该模型进行了仿真,研究了不同参数值下模型的计数概率、均值和方差的变化规律。本文以诊所病人到达时间和百货商店顾客到达时间的真实数据集为例说明了所提出模型的使用。
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引用次数: 2
Bayesian Inference and Prediction for Normal Distribution Based on Records 基于记录的正态分布贝叶斯推理与预测
IF 1.9 Pub Date : 2018-07-12 DOI: 10.6092/ISSN.1973-2201/7301
A. Asgharzadeh, R. Valiollahi, A. Fallah, S. Nadarajah
Based on record data, the estimation and prediction problems for normal distribution have been investigated by several authors in the frequentist set up. However, these problems have not been discussed in the literature in the Bayesian context. The aim of this paper is to consider a Bayesian analysis in the context of record data from a normal distribution. We obtain Bayes estimators based on squared error and linear-exponential (Linex) loss functions. It is observed that the Bayes estimators can not be obtained in closed forms. We propose using an importance sampling method to obtain Bayes estimators. Further, the importance sampling method is also used to compute Bayesian predictors of future records. Finally, a real data analysis is presented for illustrative purposes and Monte Carlo simulations are performed to compare the performances of the proposed methods. It is shown that Bayes estimators and predictors are superior than frequentist estimators and predictors.
基于记录数据,几位作者在频率表设置中研究了正态分布的估计和预测问题。然而,这些问题并没有在贝叶斯背景下的文献中进行讨论。本文的目的是在正态分布的记录数据的背景下考虑贝叶斯分析。我们得到了基于平方误差和线性指数(Linex)损失函数的贝叶斯估计量。观察到Bayes估计量不能以闭形式得到。我们建议使用重要性抽样方法来获得贝叶斯估计量。此外,重要性抽样方法也用于计算未来记录的贝叶斯预测因子。最后,为了便于说明,对实际数据进行了分析,并进行了蒙特卡洛模拟,以比较所提出方法的性能。结果表明,Bayes估计量和预测量优于频繁度估计量和估计量。
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引用次数: 1
Inference Based on k-Record Values from Generalized Exponential Distribution 基于广义指数分布k记录值的推理
IF 1.9 Pub Date : 2018-07-12 DOI: 10.6092/ISSN.1973-2201/7495
Manoj Chacko, Laji Muraleedharan
In this paper, the lower k-record values arising from a two parameter generalized exponential distribution is considered. The maximum likelihood estimators for the shape parameter and scale parameter are obtained. The Bayes estimates of the parameters are also developed by using Markov chain Monte Carlo method under symmetric and asymmetric loss functions. Finally, a simulation study is performed to find the performance of different estimators developed in this paper.
本文考虑了由两参数广义指数分布引起的较低k记录值。得到了形状参数和尺度参数的最大似然估计量。在对称和非对称损失函数下,利用马尔可夫链蒙特卡罗方法对参数进行了贝叶斯估计。最后,对本文开发的不同估计器的性能进行了仿真研究。
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引用次数: 5
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Statistica
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