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971.
AbstractFrailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor(frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set. 相似文献
972.
ABSTRACTThe shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of a random factor (frailty) and the baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and the distribution of frailty. In this paper, we consider inverse Gaussian distribution as frailty distribution and three different baseline distributions, namely the generalized Rayleigh, the weighted exponential, and the extended Weibull distributions. With these three baseline distributions, we propose three different inverse Gaussian shared frailty models. We also compare these models with the models where the above-mentioned distributions are considered without frailty. We develop 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. A search of the literature suggests that currently no work has been done for these three baseline distributions with a shared inverse Gaussian frailty so far. We also apply these three models by using a real-life bivariate survival data set of McGilchrist and Aisbett (1991) related to the kidney infection data and a better model is suggested for the data using the Bayesian model selection criteria. 相似文献
973.
ABSTRACTA new discrete distribution that depends on two parameters is introduced in this article. From this new distribution the geometric distribution is obtained as a special case. After analyzing some of its properties such as moments and unimodality, recurrences for the probability mass function and differential equations for its probability generating function are derived. In addition to this, parameters are estimated by maximum likelihood estimation numerically maximizing the log-likelihood function. Expected frequencies are calculated for different sets of data to prove the versatility of this discrete model. 相似文献
974.
Peer Bilal Ahmad 《统计学通讯:理论与方法》2013,42(12):3612-3624
ABSTRACTIn this paper, we derive the Bayes estimators of functions of parameters of the size-biased generalized power series distribution under squared error loss function and weighted square error loss function. The results of size-biased GPSD are then used to obtain particular cases of the size-biased negative binomial, size-biased logarithmic series, and size-biased Poisson distributions. These estimators are better than the classical minimum variance unbiased estimators in the sense that they increase the range of the estimation. Finally, an example is provided to illustrate the results and a goodness of fit test is done using the maximum likelihood and Bayes estimators. 相似文献
975.
AbstractIn this article, we investigate the tail propertiesof the generalized Maxwell distribution and gain an asymptoticbehavior of its Mills-type ratio. Meanwhile, we show two applications. The first application thinks about the asymptotic property of the ratio of density functions and the ratio of the tails of the generalized Maxwell and classical Maxwell distributions. Another application obtains the asymptotic distribution of the partial maximum of an independent and identically distributed sequence from the distribution. 相似文献
976.
A. K. Md. Ehsanes Saleh 《统计学通讯:理论与方法》2013,42(11):3145-3157
ABSTRACTThis article considers the estimation of a distribution function FX(x) based on a random sample X1, X2, …, Xn when the sample is suspected to come from a close-by distribution F0(x). The new estimators, namely the preliminary test (PTE) and Stein-type estimator (SE) are defined and compared with the “empirical distribution function” (edf) under local departure. In this case, we show that Stein-type estimators are superior to edf and PTE is superior to edf when it is close to F0(x). As a by-product similar estimators are proposed for population quantiles. 相似文献
977.
AbstractIn this paper, we introduce a version of Hayter and Tsui's statistical test with double sampling for the vector mean of a population under multivariate normal assumption. A study showed that this new test was more or as efficient than the well-known Hotelling's T2 with double sampling. Some nice features of Hayter and Tsui's test are its simplicity of implementation and its capability of identifying the errant variables when the null hypothesis is rejected. Taking that into consideration, a new control chart called HTDS is also introduced as a tool to monitor multivariate process vector mean when using double sampling. 相似文献
978.
Serkan Eryilmaz 《统计学通讯:理论与方法》2013,42(19):5628-5636
ABSTRACTLet (Xi, Yi), i = 1, …, n be a pair where the first coordinate Xi represents the lifetime of a component, and the second coordinate Yi denotes the utility of the component during its lifetime. Then the random variable Y[r: n] which is known to be the concomitant of the rth order statistic defines the utility of the component which has the rth smallest lifetime. In this paper, we present a dynamic analysis for an n component system under the above-mentioned concomitant setup. 相似文献
979.
980.
ABSTRACTRandom vectors with positive components are common in many applied fields, for example, in meteorology, when daily precipitation is measured through a region Marchenko and Genton (2010). Frequently, the log-normal multivariate distribution is used for modeling this type of data. This modeling approach is not appropriate for data with high asymmetry or kurtosis. Consequently, more flexible multivariate distributions than the log-normal multivariate are required. As an alternative to this distribution, we propose the log-alpha-power multivariate and log-skew-normal multivariate models. The first model is an extension for positive data of the fractional order statistics model Durrans (1992). The second one is an extension of the log-skew-normal model studied by Mateu-Figueras and Pawlowsky-Glahn (2007). We study parameter estimation for these models by means of pseudo-likelihood and maximum likelihood methods. We illustrate the proposal analyzing a real dataset. 相似文献