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Unit-Gompertz Distribution with Applications 单位- gompertz分布与应用
IF 1.9 Pub Date : 2019-07-01 DOI: 10.6092/ISSN.1973-2201/8497
J. Mazucheli, A. Menezes, S. Dey
The transformed family of distributions are sometimes very useful to explore additional properties of the phenomenons which non-transformed (baseline) family of distributions cannot. In this paper, we introduce a new transformed model, called the unit-Gompertz (UG) distribution which exhibit right-skewed (unimodal) and reversed-J shaped density while the hazard rate has constant, increasing, upside-down bathtub and then bathtub shaped hazard rate. Some statistical properties of this new distribution are presented and discussed. Maximum likelihood estimation for the parameters that index UG distribution are derived along with their corresponding asymptotic standard errors. Monte Carlo simulations are conducted to investigate the bias, root mean squared error of the maximum likelihood estimators as well as the coverage probability. Finally, the potentiality of the model is presented and compared with three others distributions using two real data sets.
变换后的分布族有时对探索现象的附加性质非常有用,而非变换(基线)分布族不能。在本文中,我们引入了一个新的转换模型,称为单位Gompertz(UG)分布,它表现出右偏(单峰)和反向J形密度,而危险率有恒定的、增加的、倒置的浴缸,然后是浴缸形危险率。给出并讨论了这种新分布的一些统计性质。导出了UG分布参数的最大似然估计及其相应的渐近标准误差。蒙特卡罗模拟研究了最大似然估计量的偏差、均方根误差以及覆盖概率。最后,利用两个真实数据集,给出了该模型的潜力,并与其他三种分布进行了比较。
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引用次数: 70
Estimation of Dynamic Cumulative Past Entropy for Power Function Distribution 幂函数分布的动态累积过去熵估计
IF 1.9 Pub Date : 2019-03-21 DOI: 10.6092/ISSN.1973-2201/7819
E. I. Abdul-Sathar, G. S. Sathyareji
In this paper, we proposed MLE and Bayes estimators of parameters and DCPE for the two parameter power function distribution. Bayes estimators under different loss functions are obtained using Lindley approximation method and important sampling procedures. A real life data set and a Monte Carlo simulation are used to study the performance of the estimators derived in the article.
本文针对两参数幂函数分布,提出了参数的MLE估计和Bayes估计,以及DCPE估计。利用Lindley近似法和重要的采样步骤,得到了不同损失函数下的Bayes估计量。用实际数据集和蒙特卡罗模拟来研究本文所导出的估计器的性能。
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引用次数: 2
Estimation of Stress-Strength Reliability for the Pareto Distribution Based on Upper Record Values 基于上记录值的Pareto分布应力-强度可靠性估计
IF 1.9 Pub Date : 2019-03-21 DOI: 10.6092/ISSN.1973-2201/8242
Rahmath Manzil Juvairiyya, P. Anilkumar
In this paper, the estimation of stress-strength reliability based on upper record values is considered when X and Y are independent random variables having a Pareto distribution with the same scale parameter and with different shape parameters. The maximum likelihood estimator (MLE), the approximate Bayes estimators and the exact confidence interval of the stress-strength reliability are obtained. A Monte Carlo simulation study is conducted to investigate the merits of the proposed methods. A real data analysis is presented for illustrative purpose.
本文考虑X和Y为具有相同尺度参数和不同形状参数的Pareto分布的独立随机变量时,基于上记录值的应力-强度可靠度估计。得到了最大似然估计量(MLE)、近似贝叶斯估计量和应力-强度可靠性的精确置信区间。通过蒙特卡罗仿真研究,验证了所提方法的优点。为了说明问题,本文给出了一个真实的数据分析。
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引用次数: 6
Discrete power distributions and inference using likelihood 离散功率分布和使用似然的推理
IF 1.9 Pub Date : 2019-03-21 DOI: 10.6092/ISSN.1973-2201/8598
A. Pallini
Discrete power distributions are proposed and studied, by considering the positive jumps on the discontinuities of an original discrete distribution function. Inequalities in moments and distribution functions are studied, allowing the definition of discrete intermediate distributions that lie between an original distribution and a power distribution. Original uniform, binomial, Poisson, negative binomial, and hypergeometric distributions are considered, to propose new power and intermediate distributions. Stochastic orders and unimodality are discussed. Estimation problems using likelihood are investigated. Simulation experiments are performed, to evaluate the bias and the mean square error of the maximum likelihood estimates, that are numerically calculated, with classic tools for numerical optimization.
通过考虑原始离散分布函数的不连续性上的正跳,提出并研究了离散功率分布。研究了矩和分布函数中的不等式,允许定义位于原始分布和幂分布之间的离散中间分布。考虑了原始的均匀分布、二项分布、泊松分布、负二项分布和超几何分布,提出了新的幂分布和中间分布。讨论了随机序和单峰性。研究了使用似然的估计问题。使用经典的数值优化工具进行了模拟实验,以评估数值计算的最大似然估计的偏差和均方误差。
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引用次数: 0
The Extended Exponentiated Weibull Distribution and its Applications 扩展指数威布尔分布及其应用
IF 1.9 Pub Date : 2019-03-21 DOI: 10.6092/ISSN.1973-2201/7503
E. Mahmoudi, R. Meshkat, Batool Kargar, D. Kundu
In this paper, we introduce a univariate four-parameter distribution. Several known distributions like exponentiated Weibull or extended generalized exponential distribution can be obtained as special case of this distribution. The new distribution is quite flexible and can be used quite effectively in analysing survival or reliability data. It can have a decreasing, increasing, decreasing-increasing-decreasing (DID), upside-down bathtub (unimodal) and bathtub-shaped failure rate function depending on its parameters. We provide a comprehensive account of the mathematical properties of the new distribution. In particular, we derive expressions for the moments, mean deviations, Renyi and Shannon entropy. We discuss maximum likelihood estimation of the unknown parameters of the new model for censored and complete sample using the profile and modified likelihood functions. One empirical application of the new model to real data are presented for illustrative purposes.
本文引入了一种单变量四参数分布。作为这种分布的特殊情况,可以得到一些已知的分布,如指数威布尔分布或扩展广义指数分布。新的分布非常灵活,可以非常有效地用于分析生存或可靠性数据。根据其参数的不同,可具有减小、增大、减小-增大-减小(DID)、倒浴盆(单峰)和浴盆形故障率函数。我们对新分布的数学性质作了全面的说明。特别是,我们推导了矩、平均偏差、Renyi和Shannon熵的表达式。我们讨论了用轮廓函数和修正似然函数对截尾样本和完全样本的新模型的未知参数的最大似然估计。为了说明目的,提出了新模型在实际数据中的一个经验应用。
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引用次数: 1
Parameterization of Continuous Covariates in the Poisson Capture-Recapture Log Linear Model for Closed Populations 封闭种群泊松捕获-重捕获对数线性模型中连续协变量的参数化
IF 1.9 Pub Date : 2019-01-01 DOI: 10.6092/ISSN.1973-2201/9854
G. Rossi, P. Pepe, O. Curzio, M. Marchi
The capture-recapture method is widely used by epidemiologists to estimate the size of hidden populations using incomplete and overlapping lists of subjects. Closed populations, heterogeneity of inclusion probabilities and dependence between lists are taken into consideration in this work. The main objective is to propose a new parameterization for the Poisson log linear odel (LLM) to treat continuous covariates in their original measurement scale. The analytic estimate of the confidence bounds of the hidden population is also provided. Proposed model was applied to simulated and real capture-recapture data and compared with the multinomial conditional logit model (MCLM). The proposed model is very similar to the MCLM in dealing with continuous covariates and the analytic confidence interval performs better than the bootstrap estimate in case of small sample size.
流行病学家广泛使用捕获-再捕获方法,通过使用不完整和重叠的受试者列表来估计隐藏人群的规模。在这项工作中,考虑了封闭群体、包含概率的异质性和列表之间的依赖性。本文的主要目的是为泊松对数线性模型(LLM)提出一种新的参数化方法来处理连续协变量的原始测量尺度。给出了隐总体置信区间的分析估计。将该模型应用于模拟和真实的捕获-再捕获数据,并与多项条件logit模型(MCLM)进行比较。该模型在处理连续协变量方面与MCLM非常相似,并且在小样本量情况下,分析置信区间优于自举估计。
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引用次数: 2
Quantile Based Relevation Transform and its Properties 基于分位数的释放变换及其性质
IF 1.9 Pub Date : 2018-12-21 DOI: 10.6092/ISSN.1973-2201/8211
Dileep Kumar Maladan, P. Sankaran, N. Nair
Relevation transform introduced by Krakowski (1973) is extensively studied in the literature. In this paper, we present a quantile based definition of the relevation transform and study its properties in the context of lifetime data analysis. We give important special cases of relevation transform in the context of proportional hazards and equilibrium models in terms of quantile function.
Krakowski(1973)提出的释放变换在文献中得到了广泛的研究。在本文中,我们提出了一个基于分位数的再激活变换的定义,并在寿命数据分析的背景下研究了它的性质。我们给出了比例风险和分位数函数平衡模型中再激活变换的重要特例。
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引用次数: 1
The Marshall-Olkin Generalized-G Family of Distributions with Applications Marshall-Olkin广义G分布族及其应用
IF 1.9 Pub Date : 2018-12-21 DOI: 10.6092/ISSN.1973-2201/7662
H. Yousof, A. Afify, S. Nadarajah, G. Hamedani, G. Aryal
We introduce a new class of distributions called the Marshall-Olkin generalized-G family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, order statistics are discussed. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.
我们引入了一类新的分布,称为Marshall-Olkin广义G族。讨论了它的一些数学性质,包括常矩和不完全矩的显式表达式、阶统计量。最大似然法用于估计模型参数。通过对实际数据集的两个应用说明了新族的重要性和灵活性。
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引用次数: 43
On the Adjustment of Non-Response through Imputation for Estimating Current Mean in Repeated Surveys 重复测量中估计当前均值的无响应脉冲平差
IF 1.9 Pub Date : 2018-12-21 DOI: 10.6092/ISSN.1973-2201/6930
Priyanka Singh, A. Singh, V. Singh
In this paper we have proposed an imputation method based on a family of factor-type estimator to deal with the problem of non-response assuming that the target population has been sampled at two different occasions. The aim is to estimate the current population mean on the basis of matching the sample from the previous occasion and on the basis of fresh sample selected at the current occasion. It has been assumed that the non-response is exhibited by the population at both the occasions and, therefore, the imputation of missing values is required in both the samples, namely, matched sample and fresh sample. Accordingly, a combined point estimator has been suggested after imputation which generates a one-parameter family of estimators. The properties of the estimator have been investigated and the replacement policy has been discussed. Finally, the comparison of the proposed class has been made with another estimator for their performances.
本文提出了一种基于因子型估计量的归算方法,以处理在两个不同场合采样的目标人群的无响应问题。其目的是在匹配前一场合的样本和在当前场合选择的新样本的基础上估计当前总体均值。假设在这两种情况下,总体都表现出不响应,因此,在两个样本中,即匹配样本和新鲜样本中,都需要对缺失值进行imputation。在此基础上,本文提出了一种组合点估计方法,该方法可以生成一组单参数估计量。研究了估计器的性质,并讨论了替换策略。最后,将所提类与另一种估计器的性能进行了比较。
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引用次数: 2
A Three Parameter Generalized Lindley Distribution: Properties and Application 三参数广义Lindley分布的性质及应用
IF 1.9 Pub Date : 2018-12-21 DOI: 10.6092/ISSN.1973-2201/8123
N. Ekhosuehi, F. Opone
In this paper, we introduced a new class of lifetime distribution and considered the mathematical properties of one of the sub models called a three parameter generalized Lindley distribution (TPGLD). The new class of distributions generalizes some of the Lindley family of distribution such as the power Lindley distribution, the Sushila distribution, the Lindley-Pareto distribution, the Lindley-half logistic distribution and the classical Lindley distribution. An application of the TPGLD to two real lifetime data sets reveals its superiority over the exponentiated power Lindley distribution, the exponentiated Lindley geometric distribution, the power Lindley distribution, the Lindley-exponential distribution and the classical one parameter Lindley distribution in modeling the lifetime data sets under study.
本文引入了一类新的寿命分布,并考虑了三参数广义林德利分布(TPGLD)子模型的数学性质。这类新分布推广了林德利分布族中的一些分布,如幂林德利分布、Sushila分布、林德利-帕累托分布、林德利-半logistic分布和经典林德利分布。通过对两个实际寿命数据集的应用,揭示了TPGLD在对所研究的寿命数据集建模方面优于幂次林德利分布、幂次林德利几何分布、幂次林德利分布、林德利指数分布和经典单参数林德利分布。
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引用次数: 6
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Statistica
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