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Walking
Published in Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler, Instant Notes in Sport and Exercise Biomechanics, 2019
The arms swing in a contralateral fashion in exact anti-phase to the legs, in other words the right arm reaches maximum shoulder and elbow flexion when the right leg reaches toe-off and maximum shoulder and elbow extension at right heel strike. Thus, the upper body is being rotated in the opposite direction to the pelvis. This out-of-phase action of the arms generates an opposite angular momentum value to the legs and so reduces the change in the angular momentum of the whole body. It is interesting to note that, despite the greater mass of the legs, the arms are able to generate a momentum almost equal in magnitude to that of the legs. This is possible because the arms are positioned further from the mid-line of the body and so require less mass to achieve the same moment of inertia (Equation F1.2). angular momentum (L) = moment of inertia (I) × angular velocity (ω) (Equation F1.2)
Confidence intervals based on L-moments for quantiles of the GP and GEV distributions with application to market-opening asset prices data
Published in Journal of Applied Statistics, 2021
Traditional techniques for estimating parameters of a univariate probability distribution are the moments and maximum likelihood methods. In 1990, Hosking [13] introduced an alternative tool vis-à-vis conventional moments for describing a probability distribution, termed L-moments. The estimation method based upon them became popular in analysis of extreme events, especially in environmental sciences such as hydrology, climatology, meteorology, and geophysics [18,19,24,36], but also in economics [3,4,35]. The L-moments method is in some cases preferred over the traditional methods for quantile estimation, specifically when such distributions with heavier tails than has the normal distribution as the generalized Pareto (GP) or generalized extreme-value (GEV) distributions are fitted to small sample data, as has been shown in several studies using large computer simulations [14,16,22,30]. Studies involving parameter estimation using L-moments have continued to be focused on point estimation, even though the confidence interval for an estimate is preferable because it is more informative than a point estimator.
A comparative analysis of clustering algorithms to identify the homogeneous rainfall gauge stations of Bangladesh
Published in Journal of Applied Statistics, 2020
Mohammad Samsul Alam, Sangita Paul
L-moments are latest advances in mathematical statistics based on probability weighted moments [6] that ease the estimation of frequency analysis [17]. However, in regional frequency analysis using the L-moments method, homogeneity is tested using heterogeneity measure namely H statistic [2]. The same idea is used in this study to check the homogeneity of clusters identified by the different clustering algorithms. Hosking and Wallis [8] described three versions H statistic whose are based on the three L-moments ratios L-coefficient of variation (13]. Moreover, four parameters Kappa distribution is fitted in this study to the regional datasets following Hosking and Wallis [8,9] to evaluate the homogeneity.
A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications
Published in Journal of Applied Statistics, 2020
M. El-Morshedy, M. S. Eliwa, H. Nagy
Let ith Os for an integer value of x can be expressed as follows ith Os can be expressed as follows vth moments of 21] has defined the L-moments (Lms) to summaries theoretical distribution and observed samples. He has shown that the Lms have good properties as measure of distributional shape and are useful for fitting distribution to data. Lms are expectation of certain linear combinations of Os. The Lms of the RV X can be expressed as follows X to be the quantities. Then, we can propose some statistical measures such as L-moment (Lm) of mean