![]() ![]() Micronutrients are vitamins and minerals that help build and repair the body’s structures internally. ![]() Whole grains are full of vitamins B1 (thiamine), B3 (niacin), and minerals like iron, magnesium, and selenium. Nuts, seeds, and legumes are examples of foods that contain high protein content, while leafy greens such as spinach are rich in iron and magnesium. These macronutrients make up a whole meal but can also be taken separately as food supplements. Macronutrients include carbohydrates, fats and proteins that provide energy for the body to function properly. The word “macro” means big or large, while “micronutrient” refers to smaller or minute nutrients. We need both types of nutrients but in different amounts. How to consume the right amount of macro and micro nutrients for optimum health? How to avoid health complications from consuming too much macronutrients? Consuming macro and micronutrients for healthy weight loss How to get more macro and micro nutrients in your diet? Finally, we demonstratethe computation of theBLUEs with two data sets. ![]() Further, we have developed R-code for computing the coefficients of the BLUEs of location and scale parameters based on any type II censored sample (including a complete sample) of size up to n=20 and for any choice of shape parameter α in the interval. We have tabulated theBLUE coefficients for all complete samples of size n=11(1)20 for α=1.5(0.5)2.0(1.0)5.0. α = Using these means, variances and covariances, we have extended the computation of the BLUEs of the location and scale parameters of GEDfor both complete sample and Type-II censoredsamples of size up to n=20. In this paper, using the formulae given byRaqab and Ahsanullah, we have developed R-program for computingthe means of order statistics for samples of size up to 30 and the variances andcovariances of order statistics for samples of size up to 20 for standard GE distribution for 1.5(0.5)5.0. Using these expressions they have obtained the necessary coefficients for computing the BLUEs of location and scale parameters of GE distributionfor known shape parameter 0.5(0.5)5.0 α = for complete samples of size up to 10. The application of the G test is illustrated with a numerical example.įor standard generalized exponential distribution (GED)Raqab and Ahsanullah have derived the exact forms of means, variances and covariancesof order statistics. The G test allows positive identification of exceptionally low variances. The G test appears superior to the C test in detecting effects from low variances. The power of the G test is verified for data sets of equal and unequal size. Representative critical values are tabulated for those who prefer to work from tables. ![]() The expressions are validated against literature values and through simulations in Excel. Expressions are derived to calculate upper limit as well as lower limit critical values for data sets of equal and unequal size at any significance level. We transform the C test into a more general “G test”. Cochran’s C test will not identify an outlying low variance, but may mistake a high variance for an outlier instead. It uses critical values that are only available for the upper tail of the variance distribution, at selected numbers of data sets, selected numbers of replicates per set and only at two significance levels. It only applies to data sets of equal size. It can be run on summary data using a pocket calculator. The C test is a one-sided outlier test that will identify deviant standard deviations. ISO Standard 5725 “Accuracy (trueness and precision) of measurement methods and results” recommends Cochran’s C test to numerically verify if three or more normally distributed data sets show “homogeneity of variances” or “homoscedasticity”. ![]()
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