Body posture in elderly,physically active males

The objective of this study was to evaluate the shape of anterior–posterior curvatures of the spine and to determine the values of body symmetry deviations in the frontal plane, in elderly males. The study group consisted of 34 males aged between 61 and 83 years, attending two hour-long training sessions a week. The comparative group consisted of 30 students. The photogrammetric method based on the Moire phenomenon was used to evaluate the body posture. The obtained data confirm characteristic tendencies of physiological spinal curvatures to change with the aging process. A decrease of the lumbar–sacral spinal-segment inclination and an increase of the upper thoracic spinal-segment inclination were observed in the elderly males. Whereas, the value of thoracic kyphosis lower-segment inclination was similar to the value obtained in young adult males. The stated differences indicate a flattening of lumbar lordosis and a deepening of the upper arch of thoracic kyphosis, which results in a characteristic body posture in the standing position with the head protruding and the upper trunk segment inclined. The above-mentioned observations indicate a dominance of the angular thoracic kyphosis value over the remaining spinal curvatures. These differences occur to a greater degree in elderly males.     

Testing for heteroscedasticity occuring at unknown points

This paper considers procedures for the detection of heteroscedasticity when it occurs at unknown points. First the number of points is assumed known apriori and then this assumption is relaxed so that both the position and the number of possible aberrant observations is unknown. Monte Carlo evidence is provided on the performance of both tests and they are found to perform reasonably.     

Bathtub distributions: a review

Bathtub distributions are characterized by bathtub failure rate functions . These are possibly more realisitic models than the monotone failure rate models . A systematic account of such distributions is not available and this review aims to give such an account . We give some easily verifiable conditions to check the bathtub property of a distribution along with methods to construct such distributions . We also discuss some stochastic and reliablity mechanisms which lead to bathtub distributions. These include mixtures ( stochastic failure rate models ) , series system , stochastic differential equation models and so on. We also review inference on bathtub distributions. The paper concludes with a rather exhaustive list of bathtub distributions.     

Some improved ratio type estimators of population mean and ratio in finite population sample surveys

In this paper we present a class of ratio type estimators of the population mean and ratio in a finite population sample surveys with without replacement simple random sampling design, where information on an auxiliary variate x positively correlated with the main variate y is available. Large sample approximations to mean square errors (MSE) of these estimatorsare evaluated and their MSE's are compared with the MSE of the usual ratio estimator [ybar]_R of [ybar] the population mean of y. It is shown that under certain conditions these estimators are more efficient than [ybar]_R. When a prior knowledge of the value of thecoefficient of variation, c_y, of y is at hand, ratio type estimator, say [ybar]₁ of [ybar] is proposed. It is shown, under certain conditions, that [ybar]₁ is more efficient than [ybar]_R. When values of c_y, c_x and the population correlation coefficient ρ is at hand, then we have proposed another estimator, say [ybar]₂ of [ybar], which is always better than [ybar]_R as far as the efficiency is concerned. In fact, is [ybar] ₂ is shown to be even better than [ybar]₁. Finally estimators better than the usual ratio estimator [ybar]/[xbar] of [Ybar] are given.     

The estimation of derivatives of a nonparametric regression function when the data are correlated

A kernel estimator of a derivative of arbitrary order of a nonparametric average population curve is considered for a correlated-errors model with balanced replicate measurements at each design point. Asymptotic expansions of the mean squared error are derived for two classes of correlation functions in the model. Consistency, choice of smoothing parameter, and rates of convergence are examined for the important special cases of estimating the first and second derivatives.     

Chain ratio type estimator for ratio of two population m3ans using auxiliary characters

In this paper we have proposed chain ratio type estimators for ratio of two population means using two auxiliary characters. The expressions for bias and mean square error of these estimators have been derived. A comparison of the proposed estimator with that of double sampling estimator has been made in terms of mean square error. An emperical study has also been made.