## signed mixtures [X’ed]

**F**ollowing a question on X validated, the hypoexponential distribution, I came across (for the second time) a realistic example of a mixture (of exponentials) whose density wrote as a signed mixture, i.e. involving both negative and positive weights (with sum still equal to one). Namely,

representing the density of a sum of *d* Exponential variates. The above is only well-defined when all rates differ, while a more generic definition involving matrix exponentiation exists. But the case when (only) two rates are equal can rather straightforwardly be derived by a direct application of L’Hospital rule, which my friend George considered as the number one calculus rule!

March 26, 2023 at 6:59 am

Are there any of George Casella’s lectures / talks available online? I haven’t been able to find any.

March 26, 2023 at 4:22 pm

Not that I know of, alas.