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I need to model the variable Total motile Count which describe how many million sperm cells in an entire ejaculate are motile. It is not a proper count since it is calculated as a product of other variables: sperm count(x10^6/mL) x motility(%) x volume(mL).

Therefore, it is not continuous. There are no zeroes (min=2 max=650, mean=129.56, var=10916.37). What family of distribution should I consider to model Total motile Count as response variable? I considered Gamma because the number of counts is very high and quasi-poisson distribution. What do you suggest? I tried Poisson and negative binomial (overdispersion parameter = 0.6063, CI: 0.4375-0.8403), suggesting that the latter is preferred (smallest AIC, also over Gamma). Thanks!

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If motility is constant, Total motile Count is also a Poisson distribution.

Y = sperm count(x10^6/mL) x motility(%) x volume(mL).

E[Y] = E[sperm count]*(x10^6/mL) x motility(%) x volume(mL).

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