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A graphical model or probabilistic graphical model ( PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics —particularly Bayesian statistics —and machine learning .
One of the most basic and milestone models of population growth was the logistic model of population growth formulated by Pierre François Verhulst in 1838. The logistic model takes the shape of a sigmoid curve and describes the growth of a population as exponential, followed by a decrease in growth, and bound by a carrying capacity due to ...
Population pyramid. A population pyramid (age structure diagram) or " age-sex pyramid " is a graphical illustration of the distribution of a population (typically that of a country or region of the world) by age groups and sex; it typically takes the shape of a pyramid when the population is growing. [1] Males are usually shown on the left and ...
Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History [ edit ] Population dynamics has traditionally been the dominant branch of mathematical biology , which has a history of more than 220 years, [1] although over the last century the scope of ...
The exploration of the content of a data set. The use to find structure in data. Checking assumptions in statistical models. Communicate the results of an analysis. If one is not using statistical graphics, then one is forfeiting insight into one or more aspects of the underlying structure of the data.
The empirical distribution function is an estimate of the cumulative distribution function that generated the points in the sample. It converges with probability 1 to that underlying distribution, according to the Glivenko–Cantelli theorem. A number of results exist to quantify the rate of convergence of the empirical distribution function to ...
In another usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in a way that eliminates the effects of certain gross influences, as in an anomaly time series.
Shape of a probability distribution. In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population. The shape of a distribution may be considered either descriptively, using terms ...