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Log-linear analysis is a technique used in statistics to examine the relationship between more than two categorical variables. The technique is used for both hypothesis testing and model building. In both these uses, models are tested to find the most parsimonious (i.e., least complex) model that best accounts for the variance in the observed ...
Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution. [2] [3] Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values.
In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion = + + +.
The red line represents the 'Median line', while the blue line is the 'Mean line'. This plot illustrates a dataset with a power-law relationship between the variables, represented by a concave line. When both variables are log-transformed, as shown in the right plot of Figure 1, titled 'Log-Log Linear Line with Normal Noise', the relationship ...
Semi-log plot of the Internet host count over time shown on a logarithmic scale. A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved.
As an example, in comparing different populations in the world, the variance of income tends to increase with mean income. If we consider a number of small area units (e.g., counties in the United States) and obtain the mean and variance of incomes within each county, it is common that the counties with higher mean income also have higher ...
ln(r) is the standard natural logarithm of the real number r. Arg( z ) is the principal value of the arg function; its value is restricted to (− π , π ] . It can be computed using Arg( x + iy ) = atan2 ( y , x ) .
The derivative of ln(x) is 1/x; this implies that ln(x) is the unique antiderivative of 1/x that has the value 0 for x = 1. It is this very simple formula that motivated to qualify as "natural" the natural logarithm; this is also one of the main reasons of the importance of the constant e.