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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 mathematical biology has greatly expanded. [citation needed] The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the ...
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 ...
The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.
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 ...
Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions .
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 such as "J-shaped", or numerically, using quantitative measures such as skewness and ...
The Student's t distribution plays a role in a number of widely used statistical analyses, including Student's t test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis .
The population Pearson correlation coefficient is defined in terms of moments, and therefore exists for any bivariate probability distribution for which the population covariance is defined and the marginal population variances are defined and are non-zero.