- Suppose I have a Normal Distribution with $\mu = 50$ and $\sigma^2 = 15$.
- If I "force" this Normal Distribution to only take values between the integers 0 to 100 .... I can find out the probability of this specific Normal Distribution taking values between the intervals (0,1), (1,2), (2,3) ... (98,99), (99,100)
- Informally, I could then make this into a Multinomial Probability Distribution with the same number of outcomes as intervals, alongside the corresponding probabilities of landing into any one of these given intervals
My Question: Is there a more formal mathematical way to do this? Can the Normal Distribution be transformed into some Discrete Distribution?
In a similar sense, given a Normal Distribution, a range of values, a number of $k$ bins (i.e. intervals), and the position/width for each of these $k$ bins : is there a more mathematical way that a Normal Distribution can be transformed into a similar looking Discrete Distribution (e.g. Multinomial Distribution)?
Thanks!
References:
- discrete version of normal distribution?
- Discretized normal distribution
- Is there something like a normal distribution model for discrete probability?
- Finite discrete approximation to the normal distribution
- Approximating a discrete probability distribution with a standard normal distribution
- What is the closest equivalent to a Gaussian distribution on a discrete domain?
- Can a discrete random variable be normally distributed?
