used by being added to the total log-likelihood. As the data can be viewed as an evidence that support the estimated parameters, this process can be interpreted as "support from independent evidence adds", and the log-likelihood is the "weight of evidence". Interpreting negative log-probability as information content or surprisal, the support (log-likelihood) of a model, given an event, is the negative of the surprisal of the event, given the model: a model is supported by an event to the extent that the event is unsurprising, given the model. A logarithm of a likelihood ratio is equal to the difference of the log-likelihoods: Just as the likelihood, given no event, being 1, the log-likelihood, given no event, is 0, which corresponds to the value of the empty sum: without any data, there is no support for any models. Graph The graph of the log-likelihood is called the support curve (in the univariate case).. In the multivariate case, the concept generalizes into a support surface over the parameter space. It has a relation to, but is distinct from, the support of a distribution. The term was coined by A. W. F. Edwards in the context of statistical hypothesis testing, i.e. whether or not the data "support" one hypothesis (or parameter value) being tested more than any other. The log-likelihood function being plotted is used in the computation of the score (the gradient of the log-likelihood) and Fisher information (the curvature of the log-likelihood). This, the graph has a direct interpretation in the context of maximum likelihood estimation and likelihood-ratio tests. Likelihood equations If the log-likelihood function is smooth, its gradient with respect to the parameter, known as the score and written , exists and allows for the application of differential calculus. The basic way to maximize a differentiable function is to find the stationary points (the points where the derivative is zero); since the derivative of a sum is just the sum of the derivatives, but the derivative of a product requires the product rule, it is easier to compute the stationary points of the log-likelihood of independent events than for the likelihood of independent events. The equations defined by the stationary point of the score function serve as estimating equations for the maximum likelihood estimator. In that sense, the maximum likelihood estimator is implicitly defined by the value at of the inverse function , where is the d-dimensional Euclidean space, and