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Logit transformation

\ Logit \ ˌtrænsfərˈmeɪʃən \

A mathematical transformation commonly used in longevity modeling.

The logit transformation of a probability p, denoted logit(p) is defined here.

In terms of conventional actuarial notation, we can think of the chance of someone dying aged (typically denoted qx) as being determined not just by their age but a whole host of potentially relevant factors. The logit transformation gives us a way of describing the effects of these predictive factors in a linear equation, which is mathematically much easier to handle than a non-linear equation.

The logit transform is an evolution of the basic log transformation originally proposed by Gompertz. In the world of Generalized Linear Models it is also the “natural” scale for analyzing events like the numbers dying at each age, which are expected to follow a Binomial distribution.

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