Table 1 Parameters used in a life table.
From: Life tables of annual life expectancy and mortality for companion dogs in the United Kingdom
Parameter | Definition | Equation |
|---|---|---|
\({d}_{x}\) | Number of dogs dying in the year interval [x, x + 1) | |
\({l}_{x}\) | Number of dogs living at year x (\(n\) denotes the starting point for the final year interval) | \(\sum_{i=x}^{n}{d}_{i}\) |
\({\widehat{q}}_{x}\) | Probability of dogs dying in the year interval [x, x + 1) | \({\widehat{q}}_{x}={d}_{x}/{l}_{x}\) |
\({\widehat{a}}_{x}\) | Mean fraction of last year of life lived by dogs died in the year interval [x, x + 1) | \({\widehat{a}}_{x}=\frac{\sum ({lifespan}^{*} -x)}{{d}_{x}}\) |
\({L}_{x}\) | Number of dog-years lived in the year interval [x, x + 1) | \({L}_{x}={(l}_{x}-{d}_{x})+{\widehat{a}}_{x}*{d}_{x}\) |
\({T}_{x}\) | Number of dog-years lived beyond year x | \(\sum_{i=x}^{n}{L}_{i}\) |
\({\widehat{e}}_{x}\) | Life expectancy at year x | \({\widehat{e}}_{x}={T}_{x}/{l}_{x}\) |
