Distribution of variables

The histogram is a visual representation of the distribution of variable data. 

This system of equations allows us to take account of the flow in the frontal zone and the influence of the fountain effect on the distributions of variables in the main stream zone. The equations for this rather complicated model can be solved numerically by computer. Comparison of the calculations with experimental data shows that the maximum deviations of the predicted values from the experimental points do not exceed 15 % (Fig. 4.60). 

Probability distribution models can be used to represent frequency distributions of variability or uncertainty distributions. When the data set represents variability for a model parameter, there can be uncertainty in any non-parametric statistic associated with the empirical data. For situations in which the data are a random, representative sample from an unbiased measurement or estimation technique, the uncertainty in a statistic could arise because of random sampling error (and thus be dependent on factors such as the sample size and range of variability within the data) and random measurement or estimation errors. The observed data can be corrected to remove the effect of known random measurement error to produce an error-free data set (Zheng Frey, 2005). 

The analytical plan of epidemiological studies should use descrip tive and analytical techniques in describing the sample and results. Descriptive statistics, such as frequency distributions, cross-tabulations, measures of central tendency, and variation, can help explain underlying distributions of variables and direct the assessment of appropriateness of more advanced statistical techniques. Careful weighing of study findings with respect to the design and methods helps to ensure the validity of results. 

Pharmacokinetic/pharmacodynamic modeling is a complex, iterative process involving multiple steps. Once data are collected, exploratory graphic analyses of the raw data are usually carried out to 1) detect outliers 2) explore distribution of variables and 3) assess... 

Statistical theory teaches that under the assumption that the population means of the two groups are the same (i.e. if Hq is true), the distribution of variable T depends only on the sample size but not on the value of the common mean or on the measurements population variance and thus can be tabulated independently of the particulars of any given experiment. This is the so-called Student s f-distribution. Using tables of the f-distribution, we can calculate the probability that a variable T calculated as above assumes a value greater or equal to 4.7, the value obtained in our example, given that H0 is true. This probability is <0.0001. Thus, if H0 is true, the result obtained in our experiment is extremely unlikely, although not impossible. We are forced to choose between two possible explanations to this. One is that a very unlikely event occurred. The second is that the result of our experiment is not a fluke, rather, the difference Mb — Ma is a positive number, sufficiently large to make the probability of this outcome a likely event. We elect the latter explanation and reject H0 in favor of the alternative hypothesis Hx. 

The covariate distribution models, which describe the characteristics of the population (weight, height, sex, race, etc.), must be determined and used for the creation of the study population. The virtual subjects are drawn from a probability distribution that can be one of many types (normal, lognormal, binomial, uniform) but that needs to be described in the study plan. For assignments to sex one must account for what proportion of patients will be female versus male. Furthermore, when creating this population the joint distribution of variables such as height and weight or sex and size must be accounted for. This then leads to the execution model. 

An important prerequisite for the use of descriptive statistics is the shape of the distribution of variables, that is, the frequency of values from different ranges of the variable. It is assumed in multiple regression analysis that the residuals — predicted minus observed values — are normally distributed. 

In this chapter the equations described in section 4.5 are solved to analyze the local distribution of variables such as temperature, species concentration, current density, reversible potential etc. Furthermore, the performance of the cell for various operational and geometrical conditions is explored. A schematic representation of the cell geometry considered in this chapter is depicted in Fig. 7.1. 

Main Operators Used for Spatial Distribution of Variables... 

Homogeneous distribution of variables through space (spatial operators replaced by scalars). 

Monitoring of fuel cells relies upon a set of techniques for the measurement of various variables such as potentials and currents, cell temperature, humidity level and flow rates on the two sides. In most cases, distributions of variables throughout the cell structure are determined with a view to finding more suitable operating conditions or improved design/capacities of the cell components. After examination of these techniques, the issue of water flooding is discussed, with presentation of techniques to be used for finding evidence of this undesirable phenomenon. 

Geostatistical analysis was used to construct maps of spatial distribution of variables, from which it was viewed that the positions have more unfavorable conditions the worker to stay inside the hangar, due to the thermal stress verified. 

Table 1. The random distributions of variables accepted to the Monte Carlo simulation of horizontal clearance to the bridge and their parameters. ... 

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