A weighty issue revisited: the dynamic effect of body weight on earnings and satisfaction in Germany

We estimate the relationship between changes in the body mass index (bmi) and wages or satisfaction, respectively, in a panel of German employees. In contrast to previous findings, our dynamic models indicate an inverse u-shaped association between bmi and wages. As the implied maximum occurs in the ‘overweight’ category, the positive trend in weight may not yet constitute a major limitation to productivity. Further investigation points out a stronger association among young workers and workers with jobs that are less protected. Work satisfaction of young workers is associated with bmi beyond the effect of earnings.     

Distributional and Inferential Properties of the Estimated Precision Cp Based on Multiple Samples

Process precision index C_p has been widely used in the manufacturing industry to provide numerical measures on process potential. Pearn et al. (1998) considered an unbiased estimator of C_p for one single sample. They showed that the unbiased estimator is the UMVUE. They also proposed an efficient test for C_p based on one single sample, and showed that the test is the UMP test. In this paper, we consider an unbiased estimator of C_p for multiple samples. We show that the unbiased estimator is the UMVUE of C_p, which is asymptotically efficient. We also consider an efficient test for C_p, and show that the test is the UMPtest for multiple samples. The practitioners can use the proposed test on theirin-plant applications to obtain reliable decisions.     

Shannon's Entropy and Its Generalisations Towards Statistical Inference in Last Seven Decades

Starting from the pioneering works of Shannon and Weiner in 1948, a plethora of works have been reported on entropy in different directions. Entropy‐related review work in the direction of statistical inference, to the best of our knowledge, has not been reported so far. Here, we have tried to collect all possible works in this direction during the last seven decades so that people interested in entropy, specially the new researchers, get benefited.     

On a Problem of Robbins

An early example of a compound decision problem of Robbins (1951) is employed to illustrate some features of the development of empirical Bayes methods. Our primary objective is to draw attention to the constructive role that the nonparametric maximum likelihood estimator for mixture models introduced by Kiefer & Wolfowitz (1956) can play in these developments.     

抽样估计中估计量的选择研究

经过研究证明VYPR-VYSR≤0,VYPR≤VYSR,这表明嬲抽样比率估计量比等概率抽样比率估计量有效。结合多方面分析可以得出结论：回归直线通过原点时,两种抽样方法的比率估计量与回归估计量抽样效率相等;当r〉0．5时,PPS的抽样效率一般比等概率抽样有效;当b〉a/X^-、并且r≥Gx/Gy时,等概率抽样的比率估计量比均值估计量有效。因而进行抽样调查时,一般是先估算r和a的值,当a值不等于零时,再估算b的值,最后根据上述的规则来决定选择采用哪种抽取样本的方法和抽样估计量。     

Reparameterized inverse gamma regression models with varying precision

In this article, we propose a mean linear regression model where the response variable is inverse gamma distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive response variable, as usual in the context of generalized linear models. The variance function of the proposed model has a quadratic form. The inverse gamma distribution is a member of the exponential family of distributions and has some distributions commonly used for parametric models in survival analysis as special cases. We compare the proposed model to several alternatives and illustrate its advantages and usefulness. With a generalized linear model approach that takes advantage of exponential family properties, we discuss model estimation (by maximum likelihood), black further inferential quantities and diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the obtained results. A real application using minerals data set collected by Department of Mines of the University of Atacama, Chile, is considered to demonstrate the practical potential of the proposed model.     

Smooth estimators for estimating order restricted scale parameters of two gamma distributions

We consider the problem of component-wise estimation of ordered scale parameters of two gamma populations, when it is known apriori which population corresponds to each ordered parameter. Under the scale equivariant squared error loss function, smooth estimators that improve upon the best scale equivariant estimators are derived. These smooth estimators are shown to be generalized Bayes with respect to a non-informative prior. Finally, using Monte Carlo simulations, these improved smooth estimators are compared with the best scale equivariant estimators, their non-smooth improvements obtained in Vijayasree, Misra & Singh (1995), and the restricted maximum likelihood estimators. Acknowledgments. Authors are thankful to a referee for suggestions leading to improved presentation.     

Right censoring in a discrete life model

Although there are many sophisticated models for estimation of failure rate based on censored data in continuous distributions, not much work has been done in the discrete case. We introduce a discrete model for life lengths and consider its properties. For this model, we derive the corresponding maximum likelihood estimators of the parameters under Type I and Type II right-censoring. Received May 2000     

Multinomial distributions applied to random sampling of particulate materials

When sampling a batch consisting of particulate material, the distribution of a sample estimator can be characterized using knowledge about the sample drawing process. With Bernoulli sampling, the number of particles in the sample is binomially distributed. Because this is rarely realized in practice, we propose a sampling design in which the possible samples have a nearly equal mass. Expected values and variances of the sample estimator are calculated. It is shown that the sample estimator becomes identical to the Horvitz–Thompson estimator in the case of a large batch-to-sample mass ratio and a large sample mass. Simulations and experiments were performed to test the theory. Simulations confirm that the round-off error due to the discrete nature of particles is negligible for large sample sizes. Sampling experiments were carried out with a mixture of PolyPropylene (PP) and PolyTetraFluorEthylene (PTFE) spheres suspended in a viscous medium. The measured and theoretical variations are in good agreement.     

Record values of the Lomax distribution

In this paper, firstly an introduction to the idea of record values for a sequence of independent and identically (Lomax or Pareto II) distributed random variables is given. Some of the distributional properties of these record values and moments up to second order are derived. These moments clearly depend on the location, scale and shape parameter of the Lomax distribution and two types of estlmators of these parameters, based on a series of observed record values are presented.