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Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals. The book is available freely online and is currently published by Dover. [1]
Arthur Lyon Bowley used precursors of the stemplot and five-number summary (Bowley actually used a "seven-figure summary", including the extremes, deciles and quartiles, along with the median—see his Elementary Manual of Statistics (3rd edn., 1920), p. 62 [11] – he defines "the maximum and minimum, median, quartiles and two deciles" as the ...
In Bayesian statistics, the model is extended by adding a probability distribution over the parameter space . A statistical model can sometimes distinguish two sets of probability distributions. The first set Q = { F θ : θ ∈ Θ } {\displaystyle {\mathcal {Q}}=\{F_{\theta }:\theta \in \Theta \}} is the set of models considered for inference.
An informative prior expresses specific, definite information about a variable. An example is a prior distribution for the temperature at noon tomorrow. A reasonable approach is to make the prior a normal distribution with expected value equal to today's noontime temperature, with variance equal to the day-to-day variance of atmospheric temperature, or a distribution of the temperature for ...
Probability density function (pdf) or probability density: function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
The main approaches for stepwise regression are: Forward selection, which involves starting with no variables in the model, testing the addition of each variable using a chosen model fit criterion, adding the variable (if any) whose inclusion gives the most statistically significant improvement of the fit, and repeating this process until none improves the model to a statistically significant ...
In statistics, an empirical distribution function (a.k.a. an empirical cumulative distribution function, eCDF) is the distribution function associated with the empirical measure of a sample. [1] This cumulative distribution function is a step function that jumps up by 1/n at each of the n data points. Its value at any specified value of the ...
V. Kumaran wrote the following comment regarding Elementary Principles in Statistical Mechanics: In this, he introduced the now standard concept of ‘ensemble’, which is a collection of a large number of indistinguishable replicas of the system under consideration, which interact with each other, but which are isolated from the rest of the universe.