Return to Answer

There's generally no problem with discretizing a continuous density that gives a suitable approximation to a discrete empirical distribution. If you want to be a bit more formal about it, there's a corresponding discrete distribution (or several, depending on how you round -- whether you're rounding off, truncating, or rounding up). You can define whichever discretized distribution you like and then formally fit that discrete distribution if you wish but with large range and a high minimum, that will make little difference.

However, the act of discretizing will change both the mean and the variance slightly. (If that's a concern you can go back to working with the resulting discrete distribution but it probably won't be important for your purposes.)

Once you have your parameters (given whichever sort of rounding/truncation you're using) giving a suitable discrete approximation to what you need, then simulation is as simple as generating from the continuous distribution and rounding. (For some purposes even rounding may not be necessary.)

If you wish to perform inference (testing, confidence intervals for the mean, that kind of thing) on it there can be a few wrinkles with such distributions (they're not always mathematically as convenient once discretized). However, when the numbers are never very small (as here), to a first approximation you can often get by perfectly well by simply ignoring the discretization when it's convenient to do so; for most things it won't matter much.

It may be worth computing the impact of doing so (ignoring the effect of discretizing) for anything of consequence, so that you can see whether it's worth worry about; even if you can do it algebraically you can use simulation to gauge how much it matters.

I'd warn you against casually interpreting a high p-value from a goodness of fit test as any suggestion that the approximation is sufficiently good for your purposes (and if your sample sizes are often large) the converse -- a low p-value won't necessarily imply that the approximation involved will have any substantial consequences for you. The question of "is this close enough to use" is not addressed by a p-value.

There's generally no problem with discretizing a continuous density that gives a suitable approximation to a discrete empirical distribution. If you want to be a bit more formal about it, there's a corresponding discrete distribution (or several, depending on how you round -- whether you're rounding off, truncating, or rounding up). You can define whichever discretized distribution you like and then formally fit that discrete distribution if you wish but with large range and a high minimum, that will make little difference.

However, the act of discretizing will change both the mean and the variance slightly. (If that's a concern you can go back to working with the resulting discrete distribution but it probably won't be important for your purposes.)

Once you have your parameters (given whichever sort of rounding/truncation you're using) giving a suitable discrete approximation to what you need, then simulation is as simple as generating from the continuous distribution and rounding. (For some purposes even rounding may not be necessary.)

If you wish to perform inference (testing, confidence intervals for the mean, that kind of thing) on it there can be a few wrinkles with such distributions (they're not always mathematically as convenient once discretized). However, when the numbers are never very small (as here), to a first approximation you can often get by perfectly well by simply ignoring the discretization when it's convenient to do so; for most things it won't matter much.

It may be worth computing the impact of doing so (ignoring the effect of discretizing) for anything of consequence, so that you can see whether it's worth worry about; even if you can't do it algebraically, you would be able to use simulation to gauge how much it matters.

I'd warn you against casually interpreting a high p-value from a goodness of fit test as any suggestion that the approximation is sufficiently good for your purposes (and if your sample sizes are often large) the converse -- a low p-value won't necessarily imply that the approximation involved will have any substantial consequences for you. The question of "is this close enough to use" is not addressed by a p-value.

There's generally no problem with discretizing a continuous density that gives a suitable approximation to a discrete empirical distribution. If you want to be a bit more formal about it, there's a corresponding discrete distribution (or several, depending on how you round -- whether you're rounding off, truncating, or rounding up). You can define whichever discretized distribution you like and then formally fit that discrete distribution if you wish but with large range and a high minimum, that will make little difference.

However, the act of discretizing will change both the mean and the variance slightly. (If that's a concern you can go back to working with the resulting discrete distribution but it probably won't be important for your purposes.)

Once you have your parameters (given whichever sort of rounding/truncation you're using), that give a suitable discrete approximation to what you need, then simulation is as simple as generating from the continuous distribution and rounding. (For some purposes even rounding may not be necessary.)

If you wish to perform inference (testing, confidence intervals for the mean, that kind of thing) on it there can be a few wrinkles with such distributions (they're not always mathematically as convenient once discretized). However, when the numbers are never very small (as here), to a first approximation you can often get by perfectly well by simply ignoring the discretization when it's convenient to do so; for most things it won't matter much.

It may be worth computing the impact of doing so (ignoring the effect of discretizing) for anything of consequence, so that you can see whether it's worth worry about; even if you can do it algebraically you can use simulation to gauge how much it matters.

I'd warn you against casually interpreting a high p-value from a goodness of fit test as any suggestion that the approximation is sufficiently good for your purposes (and if your sample sizes are often large) the converse -- a low p-value won't necessarily imply that the approximation involved will have any substantial consequences for you. The question of "is this close enough to use" is not addressed by a p-value.

There's generally no problem with discretizing a continuous density that gives a suitable approximation to a discrete empirical distribution. If you want to be a bit more formal about it, there's a corresponding discrete distribution (or several, depending on how you round -- whether you're rounding off, truncating, or rounding up). You can define whichever discretized distribution you like and then formally fit that discrete distribution if you wish but with large range and a high minimum, that will make little difference.

However, the act of discretizing will change both the mean and the variance slightly. (If that's a concern you can go back to working with the resulting discrete distribution but it probably won't be important for your purposes.)

Once you have your parameters (given whichever sort of rounding/truncation you're using) giving a suitable discrete approximation to what you need, then simulation is as simple as generating from the continuous distribution and rounding. (For some purposes even rounding may not be necessary.)

If you wish to perform inference (testing, confidence intervals for the mean, that kind of thing) on it there can be a few wrinkles with such distributions (they're not always mathematically as convenient once discretized). However, when the numbers are never very small (as here), to a first approximation you can often get by perfectly well by simply ignoring the discretization when it's convenient to do so; for most things it won't matter much.

It may be worth computing the impact of doing so (ignoring the effect of discretizing) for anything of consequence, so that you can see whether it's worth worry about; even if you can do it algebraically you can use simulation to gauge how much it matters.

I'd warn you against casually interpreting a high p-value from a goodness of fit test as any suggestion that the approximation is sufficiently good for your purposes (and if your sample sizes are often large) the converse -- a low p-value won't necessarily imply that the approximation involved will have any substantial consequences for you. The question of "is this close enough to use" is not addressed by a p-value.

There's generally no problem with discretizing a continuous density that gives a suitable approximation to a discrete empirical distribution. If you want to be a bit more formal about it, there's a corresponding discrete distribution (or several, depending on how you round -- whether you're rounding off, truncating, or rounding up). You can define whichever discretized distribution you like and then formally fit that discrete distribution if you wish but with large range and a high minimum, that will make little difference.

Note, however, that the act of discretizing will change both the mean and the variance slightly. (If that's a concern you can go back to working with the resulting discrete distribution but it probably won't be important for your purposes.)

If you wish to perform inference (testing, confidence intervals for the mean, that kind of thing) on it there can be a few wrinkles with such distributions (they're not always mathematically as convenient once discretized). However, when the numbers are never very small (as here), to a first approximation you can often get by perfectly well by simply ignoring the discretization when it's convenient to do so; for most things it won't matter much.

It may be worth computing the impact of doing so (ignoring the effect of discretizing) for anything of consequence, so that you can see whether it's worth worry about; even if you can do it algebraically you can use simulation to gauge how much it matters.

I'd warn you against casually interpreting a high p-value from a goodness of fit test as any suggestion that the approximation is sufficiently good for your purposes (and if your sample sizes are often large) the converse -- a low p-value won't necessarily imply that the approximation involved will have any substantial consequences for you. The question of "is this close enough to use" is not addressed by a p-value.

There's generally no problem with discretizing a continuous density that gives a suitable approximation to a discrete empirical distribution. If you want to be a bit more formal about it, there's a corresponding discrete distribution (or several, depending on how you round -- whether you're rounding off, truncating, or rounding up). You can define whichever discretized distribution you like and then formally fit that discrete distribution if you wish but with large range and a high minimum, that will make little difference.

However, the act of discretizing will change both the mean and the variance slightly. (If that's a concern you can go back to working with the resulting discrete distribution but it probably won't be important for your purposes.)

Once you have your parameters (given whichever sort of rounding/truncation you're using), that give a suitable discrete approximation to what you need, then simulation is as simple as generating from the continuous distribution and rounding. (For some purposes even rounding may not be necessary.)

If you wish to perform inference (testing, confidence intervals for the mean, that kind of thing) on it there can be a few wrinkles with such distributions (they're not always mathematically as convenient once discretized). However, when the numbers are never very small (as here), to a first approximation you can often get by perfectly well by simply ignoring the discretization when it's convenient to do so; for most things it won't matter much.

It may be worth computing the impact of doing so (ignoring the effect of discretizing) for anything of consequence, so that you can see whether it's worth worry about; even if you can do it algebraically you can use simulation to gauge how much it matters.

I'd warn you against casually interpreting a high p-value from a goodness of fit test as any suggestion that the approximation is sufficiently good for your purposes (and if your sample sizes are often large) the converse -- a low p-value won't necessarily imply that the approximation involved will have any substantial consequences for you. The question of "is this close enough to use" is not addressed by a p-value.