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Estimation of Cumulative Incidence Function in the Presence of Middle Censoring Using Improper Gompertz Distribution 利用不适当Gompertz分布估计中间滤波存在下的累积关联函数
IF 1.9 Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/12309
H. Rehman, N. Chandra
In this paper we deal with the modelling of cumulative incidence function using improper Gompertz distribution based on middle censored competing risks survival data. Together with the unknown parameters, cumulative incidence function also estimated. In classical set up, we derive the point estimates using maximum likelihood estimator and midpoint approximation methods. The asymptotic confidence interval are obtained based on asymptotic normality properties of maximum likelihood estimator. We also derive the Bayes estimates with associated credible intervals based on informative and non-informative types of priors under two loss functions such as squared error and LINEX loss functions. A simulation study is conducted for comprehensive comparison between various estimators proposed in this paper. A real life data set is also used for illustration.
本文研究了基于中截尾竞争风险生存数据的不正当Gompertz分布累积关联函数的建模问题。结合未知参数,估计了累积关联函数。在经典设置中,我们使用极大似然估计和中点逼近方法推导点估计。根据极大似然估计的渐近正态性,得到渐近置信区间。我们还在平方误差和LINEX损失函数两种损失函数下,基于信息和非信息类型的先验,推导出具有相关可信区间的贝叶斯估计。通过仿真研究,对本文提出的各种估计方法进行了综合比较。一个真实的数据集也被用于说明。
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引用次数: 1
Polynomial Columns-Parameter Symmetry Model and its Decomposition for Square Contingency Tables 平方列联表的多项式列参数对称模型及其分解
IF 1.9 Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/12090
S. Ando
This study proposes a polynomial columns-parameter symmetry model for square contingency tables with the same row and column ordinal classifications. In the proposed model, the odds for all i < j that an observation will fall in row category i and column category j instead of row category j and column category i depend on only the value of column category j . The proposed model is original because many asymmetry models in square contingency tables depend on the both values of row and column category. The proposed model constantly holds when the columns-parameter symmetry model holds; but the converse does not necessarily hold. This study shows that it is necessary to satisfy the polynomial columns-marginal symmetry model, in addition to the columns-parameter symmetry model, to satisfy the proposed model. This decomposition theorem is useful for explaining why the proposed model does not hold. Moreover, this study shows the value of likelihood ratio chi-square statistic for testing the proposed model is equal to the sum of that for testing the decomposed two models.
针对具有相同行和列序分类的平方列联表,提出了一个多项式列参数对称模型。在所提出的模型中,对于所有i<j,观察将落在行类别i和列类别j而不是行类别j和列类别i中的几率仅取决于列类别j的值。所提出的模型是独创的,因为方形列联表中的许多不对称模型都依赖于行和列类别的值。当柱参数对称模型成立时,所提出的模型始终成立;但反过来不一定成立。该研究表明,除了满足柱参数对称模型外,还需要满足多项式柱边缘对称模型才能满足所提出的模型。这个分解定理有助于解释为什么所提出的模型不成立。此外,该研究表明,用于测试所提出的模型的似然比卡方统计量的值等于用于测试分解的两个模型的似然比卡方统计量值的和。
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引用次数: 0
The Marshall-Olkin Gompertz Distribution: Properties and Applications Marshall-Olkin-Gompertz分布:性质与应用
IF 1.9 Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/10993
J. T. Eghwerido, Joel Oruaoghene Ogbo, Adebola Evelyn Omotoye
This article introduces three parameters class for lifetime Poisson processes in the Marshall-Olkin transformation family that are increasing, bathtub and skewed. Some structural mathematical properties of the Marshall-Olkin Gompertz (MO-G) model were derived. The MO-G model parameters were established by maximum likelihood approach. The flexibility, efficiency, and behavior of the MO-G model estimators were examined through simulation. The empirical applicability, flexibility and proficiency of the MO-G model was scrutinized by a real-life dataset. The proposed MO-G model provides a better fit when compared to existing models in statistical literature and can serve as an alternative model to those appearing in modeling Poisson processes.
本文介绍了Marshall-Olkin变换族中寿命泊松过程的三个参数类,即递增、浴缸和偏斜。导出了Marshall-Olkin-Gompertz(MO-G)模型的一些结构数学性质。采用最大似然法建立了MO-G模型参数。通过仿真检验了MO-G模型估计器的灵活性、效率和行为。MO-G模型的经验适用性、灵活性和熟练程度通过真实数据集进行了仔细检查。与统计文献中的现有模型相比,所提出的MO-G模型提供了更好的拟合,并且可以作为泊松过程建模中出现的模型的替代模型。
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引用次数: 2
A Class of Univariate Non-Mesokurtic Distributions Using a Continuous Uniform Symmetrizer and Chi Generator 一类使用连续均匀对称器和Chi发生器的单变量非中丘分布
IF 1.9 Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/12336
Kamala Naganathan Radhalakshmi, M. L. William
In a good number of real life situations, the observations on a random variable of interest tend to concentrate either too closely or too thinly around a central point but symmetrically like the normal distribution. The symmetric structure of the density function appears like that of a normal distribution but the concentration of the observations can be either thicker or thinner around the mean. This paper attempts to generate a family of densities that are symmetric like normal butwith different kurtosis. Drawing inspiration from a recent work on multivariate leptokurtic normal distribution, this paper seeks to consider the univariate case and adopt a different approach to generate a family to be called ’univariate non-mesokurtic normal’ family.The symmetricity of the densities is brought out by a uniform random variable while the kurtosis variation is brought about by a chi generator. Some of the properties of the resulting class of distributions and the pameter estimation are discussed.
在许多实际情况下,对感兴趣的随机变量的观察倾向于过于紧密或过于分散地集中在一个中心点周围,但像正态分布一样对称。密度函数的对称结构看起来像正态分布,但在平均值附近,观测值的浓度可能更厚,也可能更薄。本文试图生成一组像正态一样对称但峰度不同的密度。从最近关于多变量细峰正态分布的研究中获得灵感,本文试图考虑单变量情况,并采用不同的方法来生成一个称为“单变量非中丘正态”族。密度的对称性由均匀随机变量引起,峰度变化由chi发生器引起。讨论了所得到的一类分布的一些性质和参数估计。
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引用次数: 0
A New Discrete Distribution: Properties, Characterizations, Modeling Real Count Data, Bayesian and Non-Bayesian Estimations 一种新的离散分布:性质、表征、实数数据建模、贝叶斯和非贝叶斯估计
IF 1.9 Pub Date : 2021-10-26 DOI: 10.6092/ISSN.1973-2201/11635
H. Yousof, C. Chesneau, G. Hamedani, M. Ibrahim
In this work, a new discrete distribution which includes the discrete Burr-Hatke distribution is defined and studied. Relevant statistical properties are derived. The probability mass function of the new distribution can be "right skewed" with different shapes, bimodal and "uniformed". Also, the corresponding hazard rate function can be "monotonically decreasing", "upside down", "monotonically increasing", "upside down increasing", and "upside down-constant-increasing". A numerical analysis for the mean, variance, skewness, kurtosis and the index of dispersion is presented. The new distribution could be useful in the modeling of "under-dispersed" or "overdispersed" count data. Certain characterizations of the new distribution are presented. These characterizations are based on the conditional expectation of a certain function of the random variable and in terms of the hazard rate function. Bayesian and non-Bayesian estimation methods are considered. Numerical simulations for comparing Bayesian and non-Bayesian estimation methods are performed. The new model is applied for modeling carious teeth data and counts of cysts of kidneys data.
本文定义并研究了一种新的离散分布,其中包括离散Burr-Hatke分布。导出了相关的统计性质。新分布的概率质量函数可以是不同形状的“右偏斜”、双峰和“均匀”分布。相应的风险率函数可以是“单调递减”、“倒挂递增”、“倒挂递增”、“倒挂递增”、“倒挂递增”。给出了均值、方差、偏度、峰度和离散度指数的数值分析。新的分布可以用于“欠分散”或“过度分散”计数数据的建模。提出了新分布的某些特征。这些特征是基于随机变量的某个函数的条件期望和风险率函数。考虑了贝叶斯和非贝叶斯估计方法。对贝叶斯估计方法和非贝叶斯估计方法进行了数值模拟比较。将该模型应用于龋齿数据和肾囊肿计数数据的建模。
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引用次数: 11
The Zografos-Balakrishnan Lindley Distribution: Properties and Applications Zografos-Balakrishnan-Lindley分布的性质与应用
IF 1.9 Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/11101
M. Irshad, Veena D’cruz, R. Maya
The Lindley distribution was proposed in the context of Bayesian statistics as a counter example of fiducial statistics. In this paper, we propose Zografos Balakrishnan Lindley (ZBL) distribution in which Lindley distribution is a special case. Some properties of the new distribution is obtained such as moments, hazard rate function, reliability function etc. The parameters are estimated using the method of maximum likelihood. Finally an application of the proposed distribution to a real data set is illustrated and it is concluded that Zogarfos Balakrishnan Lindley (ZBL) distribution provides better fit than other classical distributions.
林德利分布是在贝叶斯统计的背景下提出的,作为基准统计的反例。本文提出了Zografos Balakrishnan Lindley (ZBL)分布,其中Lindley分布是一个特例。得到了新分布的矩、危险率函数、可靠度函数等性质。采用最大似然法对参数进行估计。最后给出了该分布在实际数据集上的应用,结果表明Zogarfos - Balakrishnan - Lindley (ZBL)分布比其他经典分布具有更好的拟合性。
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引用次数: 4
Robust Estimations of Survival Function for Weibull Distribution 威布尔分布生存函数的鲁棒估计
IF 1.9 Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/12433
D. Karagöz, N. A. Tutkun
The aim of this study is to estimate the robust survival function for the Weibull distribution. Since the survival function of Weibull distribution is based on the parameters, we consider two robust and explicit Weibull parameter estimators proposed by Boudt et al. (2011). The quantile and the quantile least squares which are all robust to censored data is used as an alternative to the maximum likelihood estimation of the Weibull parameters. The proposed estimators are applied to Hodgin’s disease data which produces smaller variances for the robust survival function. The advantage of new methods is that they are numerically explicit in applications. Monte Carlo simulation is performed to compare the behaviours of the proposed robust estimators in the presence of right, left and interval censored observations considering different censoring rates. The simulation results show that the proposed robust estimators are better than the maximum likelihood estimator.
本研究的目的是估计威布尔分布的鲁棒生存函数。由于威布尔分布的生存函数是基于参数的,我们考虑了Boudt et al.(2011)提出的两个鲁棒和显式威布尔参数估计器。分位数和分位数最小二乘对截尾数据都具有鲁棒性,可用来替代威布尔参数的极大似然估计。所提出的估计量应用于霍奇金病数据,该数据对鲁棒生存函数产生较小的方差。新方法的优点是它们在应用程序中是数字显式的。通过蒙特卡罗仿真比较了所提出的鲁棒估计器在考虑不同审查率的右、左和区间审查观测值存在下的行为。仿真结果表明,所提出的鲁棒估计量优于极大似然估计量。
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引用次数: 0
Muth Distribution and Estimation of a Parameter Using Order Statistics 用序统计量估计参数的分布和估计
IF 1.9 Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/9432
M. Irshad, R. Maya, Sasikumar Arun
In this work, we have considered a lifetime distribution namely Muth distribution and pointed out instances where it appears as a good model to study the stochastic nature of the variable under consideration. We have derived the best linear unbiased estimator (BLUE) of the scale parameter of the Muth distribution based on order statistics for some known values of the shape parameter.We have further estimated the scale parameter of Muth distribution by U-statistics  based on best linear functions of order statistics as kernels. The efficiency of the BLUE relative to the usual unbiased estimator has been also evaluated. An illustration describing the performance of U-statistics estimation method when compared with the classical maximum likelihood method is also given.
在这项工作中,我们考虑了一个寿命分布,即Muth分布,并指出了它作为一个很好的模型来研究所考虑的变量的随机性质的实例。对于已知形状参数的一些值,我们基于序统计量导出了Muth分布尺度参数的最佳线性无偏估计量(BLUE)。以序统计量的最佳线性函数为核,进一步用u统计量估计了Muth分布的尺度参数。与通常的无偏估计器相比,BLUE的效率也得到了评估。并举例说明了u统计估计方法与经典极大似然估计方法的性能。
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引用次数: 1
Characterization of Generalized Distribution by Doubly Truncated Moment 用双截矩刻画广义分布
IF 1.9 Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/10718
Haseeb Athar, Y. Abdel-Aty, M. A. Ali
In this paper characterization properties based on conditional expectation of a continuous function of random variable are studied when truncation is from both the sides, left and right. Then, these results are applied to obtain the k-th doubly truncated moment for a general class of distribution. Further, some examples and particular cases based on this general class of distributions are also demonstrated. The results are obtained in simple and explicit manner which also unifies the earlier results obtained by several authors. In the end, simulation study is performed to validate the correctness of theoretical characterization results and then two real life data sets are used to demonstrate the applications of these results.
本文研究了随机变量连续函数在左右两侧截断时基于条件期望的特征性质。然后,将这些结果应用于获得一类一般分布的第k个双截矩。此外,还展示了基于这类一般分布的一些例子和特殊情况。结果是以简单明了的方式获得的,这也统一了几位作者早期获得的结果。最后,通过仿真研究验证了理论表征结果的正确性,并用两个实际数据集验证了这些结果的应用。
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引用次数: 0
A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference 一个柔性浴盆形失效时间模型的性质及相关推断
IF 1.9 Pub Date : 2021-09-03 DOI: 10.6092/ISSN.1973-2201/10025
N. Choudhary, Abhishek Tyagi, B. Singh
In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.
在本研究中,我们引入了一个带有额外形状参数的修正威布尔分布的扩展版本,以便为其密度和危险率函数提供更大的灵活性。该分布能够模拟出浴缸型、递减型、递增型和恒定型的危险率函数。该模型包含了在生命周期数据分析中广泛使用的子模型,如修正Weibull、Chen、极值、Weibull、Rayleigh和指数分布。我们研究了它的统计性质,包括危险率函数、矩和阶统计量的分布。采用极大似然法和贝叶斯估计法对模型中涉及的参数进行估计。在贝叶斯估计中,我们假设参数具有独立的Gamma先验,并采用Gibbs采样器中的Metropolis-Hastings算法等MCMC技术来获得基于样本的估计量和参数的最高后验密度区间。Tierney and Kadane(1986)近似也用于获得参数的贝叶斯估计。为了突出所获得的各种估计的相对重要性,进行了模拟研究。用两个实际数据集说明了该模型的有效性。
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引用次数: 0
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Statistica
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