Then its no longer a poisson distribution because the very definition of a poisson distribution is thatgleem said:
The Poisson distribution is a probability distribution that is used to model the number of times an event occurs in a fixed interval of time or space. It is often used in situations where the probability of an event occurring is small, but the number of opportunities for the event to occur is large.
The variation coefficient, also known as the coefficient of variation, is a measure of the relative variability of a dataset. In a Poisson distribution, a variation coefficient of .5 means that the standard deviation is half of the mean, indicating a moderate level of variation in the data.
The variation coefficient in a Poisson distribution is calculated by dividing the standard deviation by the mean. This gives a measure of the relative variability of the data, allowing for comparison between datasets with different means and standard deviations.
Yes, a Poisson distribution can have a variation coefficient greater than 1. This indicates a high level of variability in the data, with the standard deviation being larger than the mean. In these cases, the Poisson distribution may not be the best fit for the data and alternative distributions should be considered.
The variation coefficient can affect the shape of a Poisson distribution in that a higher variation coefficient will result in a wider and flatter distribution, while a lower variation coefficient will result in a narrower and taller distribution. This is because a higher variation coefficient indicates a higher level of variability in the data, resulting in a wider spread of values around the mean.