Problem: Given a bounded Gaussian Distribution -- looking reproduce similar results i.e. same mean and standard deviation randomly.
Definition: Data set exhibits properties of a Gaussian distribution. Data set is bounded. Each value of the data set is an integer.
Let mu and sigma represent the mean and standard deviation. Let a and b represent the lower and upper bounds.
Comments: Tried to employ both rtnorm or rttruncnorm functions in R programming.
When I get a value from either of these functions, I'm simply rounding the result to the nearest integer. When I elect to unbound either function ie. from -Inf to Inf, I find that I can reproduce an experimental data set that is quite similar to the original data except for having data values that are obviously falling outside of the original boundaries [a,b], but yes do achieve the goal mu and sigma.
When I bound my result using these functions, the effective standard deviation is smaller as compared to the original standard deviation; I'm cutting away the head and tail of the distribution leaving an effective sigma that spans a smaller range.
While I appreciate that I can multiply and shift between truncated and non-truncated distributions using (X-mu)/sigma where X is a random value, the real goal is to reproduce an experimental truncated Gaussian distribution corresponding to the original truncated Gaussian data set.
For example, I tried simply increasing the goal standard deviation in rtnorm function for a bounded data set [a,b] to generate an effective standard deviation that is equivalent to the original standard deviation; however, this approach failed. This resulted in the standard deviation increasing somewhat but the effective standard deviation hit a ceiling falling short of the goal sigma thus never realizing the original standard deviation, mean and boundaries.
Remember, I am going on the premise that since I have an actual, real-world bounded Gaussian distribution with a given mean and standard deviation, I'm thinking that I can absolutely reproduce a similar randomly generated result.
Am I mistaken? What might I do differently?
I appreciate any insight that any of you might lend. Your help would really be welcomed and valued.