Editing Hand formula (section)

=== Mathematical rationale ===
The Hand formula attempts to formalize the intuitive notion that when the [[Expected value|expected]] loss <math>\mathbb{E}(L)</math> exceeds the cost of taking precautions, the duty of care has been breached:<math display="block">\mathbb{E}(L) > B</math>To assess the expected loss, [[Statistics|statistical methods]], such as [[regression analysis]], may be used. A common metric for quantifying losses in the case of [[Work accident|work accidents]] is the [[present value]] of lost future earnings and medical costs associated with the accident.<ref>{{Cite book|url=https://www.litigationeconomics.com/PDF/eguide-eco-damages.pdf|title=How Economists Compute Lost Earnings and Other Economic Damages in Personal Injury Cases|last=Stephenson|first=Stanley P.|publisher=James Publishing|year=2013|access-date=2019-12-16|archive-date=2023-08-12|archive-url=https://web.archive.org/web/20230812072545/https://www.litigationeconomics.com/PDF/eguide-eco-damages.pdf|url-status=dead}}</ref> In the case when the probability of loss is assumed to be a single number <math>P</math>, and <math>L</math> is the loss from the event occurring, the familiar form of the Hand formula is recovered. More generally, for continuous outcomes the Hand formula takes form:<math display="block">\int_{\Omega} Lf(L)dL > B</math>where <math>\Omega</math> is the domain for losses and <math>f(L)</math> is the [[probability density function]] of losses. Assuming that losses are positive, common choices for loss distributions include the [[Gamma distribution|gamma]], [[Log-normal distribution|lognormal]], and [[Weibull distribution|Weibull]] distributions.