I am trying to make a function which is exponential for a while, and then turns gaussian:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

f(l,d) = \lambda e^{-\lambda d} , 0 < d < l

[/tex]

and

[tex]

f(l,d) = (1-\int_0^l \lambda e^{-\lambda d} dd) \frac{1}{\sigma \sqrt{2 \pi}} e^{-(d-l)^2/(2\sigma^2)} , l < d < \infty

[/tex]

(That is supposed to be a piecewise function!)

You can see that as a function of d, the function is exponential until l and then gives the remaining weight (ie 1 - the area accumulated so far) to the gaussian.

The problem is, interpreted as a function of l (the likelihood of l given d instead of the probability of d given l), I don't understand if it is defined, since the piecewise region depends on l.

Does that make sense?

Thanks,

Dave

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# Interesting density function

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