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The odds of an event is the ratio of the probability that the event will happen (p) to the probability that it will not happen (1-p).
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Are odds relevant for continuous random variables?
via%3Dihub
Thus, the definition of the odds applied to a continous varible $X$ can be:
$$Odds = \frac{P(X < x)}{P(X \geq x)}$$
And the odds ratio, given a discrete variable $Y$:
$$Odds = \frac{P(X < x … Check https://onlinelibrary.wiley.com/doi/epdf/10.1002/sim.1776, where they apply the odds ratio after a linear regression, without dichotomizing.
Hope it helps. …