As the parameter λ increases in a Poisson distribution, its kurtosis decreases. The distribution becomes more symmetric and bell-shaped, resembling a normal distribution, in line with the Central Limit Theorem.
As the parameter λ (lambda) of a Poisson distribution increases, the kurtosis of the distribution decreases. Kurtosis measures the tailedness of a probability distribution.
In the case of the Poisson distribution, as λ becomes larger, the distribution approaches a normal distribution. A Poisson distribution with a higher λ becomes more symmetric and bell-shaped, resembling a normal distribution with a kurtosis of 3.
As λ grows, the tails of the distribution become less pronounced, leading to a reduction in kurtosis. This convergence towards normality is consistent with the Central Limit Theorem, which states that the sum or average of a large number of independent and identically distributed random variables, even if not normally distributed, tends to follow a normal distribution.
Therefore, for large λ, the kurtosis of the Poisson distribution approaches the kurtosis of a normal distribution, which is 3.