1. The problem statement, all variables and given/known data The data contains 2500 integers, each is either a 0, 1 or 2: zeroes: 1240 ones: 1014 two's: 246 Does the data follow Poisson, geometric, binomial or negative-binomial distribution? 2. Relevant equations 3. The attempt at a solution The mean of the data is 0.6024 and the variance is 0.436314 Negative-binomial distribution is supposed to have greater variance than mean, so I only consider Poisson, binomial and geometric distributions. Poisson is supposed to have it's mean equal to it's variance. I don't know if I should reject Poisson though, after using method of moments and setting λ=0.6024 I get these theoretical values of distribution: zeroes:1369 ones:825 twos:248 It's not really that far off. However, Chi-squared test gives me a value of χ2≈55 which is very large and tells me the hypothesis that my data follows Poisson distribution should be rejected. I tried generating random Poisson distribution values with λ=0.6024 and got zeroes:1348 ones:880 twos:214 which gives χ2≈33. Closer, but still too large. As for binomial distribution, using method of moments I get 2500*p=0.6024; p=0.000241 With this estimator, using theoretical formulas for calculating binomial probabilities I end up with these values: zeroes:1369 ones:825 twos:248 These are identical to the theoretical Poisson distribution values. However, when I try to generate 2500 binomial distribution random values with p=0.000241 I get very different results, something like: zeroes:1850 ones:531 twos:97 I don't really know why it differs. Finally, geometric distribution. I really did not know what estimators I should use for this one. I tried using (1-p)/p=0.6024 which gives theoretical values of zeroes:1506 ones:599 twos:238 The randomly generated values were very close to these, but it's quite far off from my data. So, after all, I still have no clue which distribution does my data follow. Could you help me with that?