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A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
With β = 1, the usual exponential function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is characteristically stretched, hence the name of the function. The compressed exponential function (with β > 1) has less practical importance, with the notable exception of β = 2, which gives the normal ...
On a semi-log plot the spacing of the scale on the y-axis (or x-axis) is proportional to the logarithm of the number, not the number itself. It is equivalent to converting the y values (or x values) to their log, and plotting the data on linear scales. A log–log plot uses the logarithmic scale for both axes, and hence is not a semi-log plot.
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4. The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1. The minimum value of x is ...
Used in business, science and engineering. Performs complex scalar or matrix based ODE solving with parametric optimization. Has 2D and 3D plotting, 3D animation, and state transition built in. Yorick: n/a n/a n/a 9 January 2015: Free GPL: Programmable, callable 2D+3D plotting.
Another generalized log-logistic distribution is the log-transform of the metalog distribution, in which power series expansions in terms of are substituted for logistic distribution parameters and . The resulting log-metalog distribution is highly shape flexible, has simple closed form PDF and quantile function , can be fit to data with linear ...
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
A log-linear plot or graph, which is a type of semi-log plot. Poisson regression for contingency tables, a type of generalized linear model . The specific applications of log-linear models are where the output quantity lies in the range 0 to ∞, for values of the independent variables X , or more immediately, the transformed quantities f i ( X ...