Prediction of vertical jump height from anthropometric factors in male and female martial arts athletes

BACKGROUND: Vertical jump is an index representing leg/kick power. The explosive movement of the kick is the key to scoring in martial arts competitions. It is important to determine factors that influence the vertical jump to help athletes improve their leg power. The objective of the present study is to identify anthropometric factors that influence vertical jump height for male and female martial arts athletes. METHODS: Twenty-nine male and 25 female athletes participated in this study. Participants were Malaysian undergraduate students whose ages ranged from 18 to 24 years old. Their heights were measured using a stadiometer. The subjects were weighted using digital scale. Body mass index was calculated by kg/m(2). Waist-hip ratio was measured from the ratio of waist to hip circumferences. Body fat % was obtained from the sum of four skinfold thickness using Harpenden callipers. The highest vertical jump from a stationary standing position was recorded. The maximum grip was recorded using a dynamometer. For standing back strength, the maximum pull upwards using a handle bar was recorded. Multiple linear regression was used to obtain the relationship between vertical jump height and explanatory variables with gender effect. RESULTS: Body fat % has a significant negative relationship with vertical jump height (P < 0.001). The effect of gender is significant (P < 0.001): on average, males jumped 26% higher than females did. CONCLUSION: Vertical jump height of martial arts athletes can be predicted by body fat %. The vertical jump for male is higher than for their female counterparts. Reducing body fat by proper dietary planning will help to improve leg power

Hybrid conditional plot of goodness-of-fit for Gumbel distribution

A Gumbel model is an extreme value model that describes the event of extreme behaviour. The Gumbel model has an exponential tail. Generally, the goodness-of-fit for the Gumbel model is evaluated by the graphical form of probability plot (PP) and quantiles plot (QQ). The model fits the observed values if the probability and the quantiles of the hypothetical distribution are linearly plotted against that of the observed values. However, the QQ plot is quite sensitive to the deviation at the tail of the plot, as opposed to the PP plot which is somewhat robust. Thus, distribution of extreme values is likely to deviate from the linear line at the tail of the QQ plot. An alternative approach of plotting the Gumbel model is given, in which the approach is expected to produce the linear plot. The conditional plot and stabilised plot are employed and the performances of both are compared. The plots are transformed into the hybrid plot so that the departures of the hypothetical quantiles values from the observed quantiles values are illustrated. The result shows that the hybrid conditional QQ plot is a better plot of goodness-of-fit for Gumbel model

Hypothesis tests of goodness-of-fit for Fréchet distribution

Extreme Value Theory (EVT) is a statistical field whose main focus is to investigate extreme phenomena. In EVT, Fréchet distribution is one of the extreme value distributions and it is used to model extreme events. The degree of fit between the model and the observed values was measured by Goodness-of-fit (GOF) test. Several types of GOF tests were also compared. The tests involved were Anderson-Darling (AD), Cramer-von Mises (CVM), Zhang Anderson Darling (ZAD), Zhang Cramer von-Mises (ZCVM) and Ln. The values of parameters μ, σ and ξ were estimated by Maximum Likelihood. The critical values were developed by Monte-Carlo simulation. In power study, the reliability of critical values was determined. Besides, it is of interest to identify which GOF test is superior to the other tests for Fréchet distribution. Thus, the comparisons of rejection rates were observed at different significance levels, as well as different sample sizes, based on several alternative distributions. Overall, given by Maximum Likelihood Estimation of Fréchet distribution, the ZAD and ZCVM tests are the most powerful tests for smaller sample size (ZAD for significance levels 0.05 and 0.1, ZCVM for significance level 0.01) as compared to AD, which is more powerful for larger sample size

Goodness-of-fit tests for extreme value distributions

This study concentrates on the Goodness-of-fit (GoF) test for the extreme value distributions. The distributions involved are Generalized Extreme Value (GEV) Type-I, Type-II and Type-III distributions. In this study, the types of GoF tests involved are the graphical plots as well as the statistical tests. In the graphical plot, the existing QQ plot is built based on the quantiles of the hypothetical and empirical distributions. However, the QQ plot suffers from the deviation at the tail of the distribution which particularly occurs very often for the case of heavy tailed distributions. In order to reduce the deviation, the conditional quantiles is recommended. The conditional quantiles plots the end points of the hypothetical and empirical distributions closer to each other. In addition, the alternative plot suggested is hybrid plot. Unlike the QQ plot which plots the original values of the quantiles, the hybrid plot illustrates the quantiles deviation between the hypothetical and empirical values. Moreover, the hybrid plot lets several statistical models to be plotted into a single graph. These plots are done in a graph because the degree of fit for different statistical models can be visually compared. This is because the horizontal axis is restricted between 0 to 1 for any statistical distribution. The parameters of GEV Type-I, Type-II and Type-III are estimated by maximum likelihood estimation (MLE). The statistical tests involved in the GoF test are Anderson-Darling (AD), Cramer-von Mises (CVM), Zhang Anderson-Darling (ZAD), Zhang Cramer-von Mises (ZCVM) and Shimokawa (Ln) tests. To determine the most powerful statistical test, the critical values of these statistical tests are generated first. Then, the reliability of the critical values are validated by the power study. If the rejection rate of the critical value is close to the respective significance level, that particular critical value is reliable. In addition, it is of interest to make use of the critical values developed by other researchers. These critical values are done for GEV distribution. These critical values were generated from AD, ZAD and Ahmad tests. For this study, they are labelled as AD-GEV, ZADGEV and Ahmad-GEV respectively. These critical values are tested for reliability as well. The power of the statistical tests are examined by the power study as well. Next, to evaluate the power, the alternative distributions are fitted to the extreme value distribution model. Based on the alternative distributions, the most powerful test should be able to produce the highest rejection rate. The results for graphical plot show that conditional quantiles plot is better than the traditional quantiles plot to illustrate the agreement between two identical distributions as well as the discrepancy between two different distributions. Besides,for the statistical tests, the results state that the AD test is the most powerful test for GEV Type-I. For GEV Type-II, the most powerful test are devided according to the cluster of sample size n. The AD test can generally be used for cluster n=15 to 17, while the ZAD test is powerful for the cluster n=18 to 49. The cluster of n=50 to 100 has AD-GEV test as the powerful test. Besides, for GEV Type-III,the ZAD test is generally powerful for cluster n= 18 to 100, but for cluster, n=15 to 17, the ZCVM test is more powerful. In the application part, two types of data were used. The first type is the data that was collected from extreme value distribution while the second type is the data that is normally distributed. The extreme value distribution models are fitted to both types of data. The data that is distributed according to the extreme values distribution is used to verify the agreement between the extreme value distribution and the extreme value distribution model. On the other hand, data that is normally distributed is employed to verify that extreme value distribution model does not fit the non extreme value distribution. The result signifies that the findings in graphical and statistical method of GoF are applicable

Model selection and validation of extreme distribution by goodness-of-fit test based on conditional position

In Extreme Value Theory, the important aspect of model extrapolation is to model the extreme behavior. This is because the choice of the extreme value distribution model affects the prediction that is about to be made. Thus, model validation which is called Goodness-of-fit (GoF) test is necessary. In this study, the GoF tests were used to fit the Generalized Extreme Value (GEV) Type-II model against the simulated observed values. The μ, σ and ξ were estimated by Maximum Likelihood. The critical values based on conditional points were developed by Monte-Carlo simulation. The powers of the tests were identified by power study. The data that is distributed according to GEV Type-II distribution was used to test whether the critical values developed are able to confirm the fit between GEV Type-II model and the data. To confirm the fit, the statistics value of the GOF test should be smaller than the critical value

Boundary Effect on Marangoni Convection in a Variable Viscosity Fluid Layer

The onset of Marangoni convection in a horizontal fluid layer with a free surface overlying a solid layer heated from below is studied. Problem is focused on the effect of the solid layer depth or its conductivity. The viscosity group, Rv, Biot number, Bi, depth ratio, dr and conductivity ratio, kr, are significant on determining the critical Marangoni number Mc with the corresponding critical wavenumber ac. The characteristics problem is solved numerically. Results show that the temperaturedependent viscosity destabilizes the fluid system but it behaves oppositely when a higher relative thermal conductivity ratio or higher depth ratio is taken

Prediction of Vertical Jump Height from Anthropometric Factors in Male and Female Martial Arts Athletes

Background: Vertical jump is an index representing leg/kick power. The explosive movement of the kick is the key to scoring in martial arts competitions. It is important to determine factors that influence the vertical jump to help athletes improve their leg power. The objective of the present study is to identify anthropometric factors that influence vertical jump height for male and female martial arts athletes. Methods: Twenty-nine male and 25 female athletes participated in this study. Participants were Malaysian undergraduate students whose ages ranged from 18 to 24 years old. Their heights were measured using a stadiometer. The subjects were weighted using digital scale. Body mass index was calculated by kg/m2. Waist–hip ratio was measured from the ratio of waist to hip circumferences. Body fat % was obtained from the sum of four skinfold thickness using Harpenden callipers. The highest vertical jump from a stationary standing position was recorded. The maximum grip was recorded using a dynamometer. For standing back strength, the maximum pull upwards using a handle bar was recorded. Multiple linear regression was used to obtain the relationship between vertical jump height and explanatory variables with gender effect. Results: Body fat % has a significant negative relationship with vertical jump height (P < 0.001). The effect of gender is significant (P < 0.001): on average, males jumped 26% higher than females did. Conclusion: Vertical jump height of martial arts athletes can be predicted by body fat %. The vertical jump for male is higher than for their female counterparts. Reducing body fat by proper dietary planning will help to improve leg power

Hybrid conditional plot of goodness-of-fit for gumbel distribution (Plot bersyarat hibrid bagi ujian kebagusan penyuaian untuk taburan gumbel)

A Gumbel model is an extreme value model that describes the event of extreme behaviour. The Gumbel model has an exponential tail. Generally, the goodness-of-fit for the Gumbel model is evaluated by the graphical form of probability plot (PP) and quantiles plot (QQ). The model fits the observed values if the probability and the quantiles of the hypothetical distribution are linearly plotted against that of the observed values. However, the QQ plot is quite sensitive to the deviation at the tail of the plot, as opposed to the PP plot which is somewhat robust. Thus, distribution of extreme values is likely to deviate from the linear line at the tail of the QQ plot. An alternative approach of plotting the Gumbel model is given, in which the approach is expected to produce the linear plot. The conditional plot and stabilised plot are employed and the performances of both are compared. The plots are transformed into the hybrid plot so that the departures of the hypothetical quantiles values from the observed quantiles values are illustrated. The result shows that the hybrid conditional QQ plot is a better plot of goodness-of-fit for Gumbel model