Negative binomial distribution, Advanced Statistics

Negative binomial distribution is the probability distribution of number of failures, X, before the kth success in the sequence of Bernoulli trials where the probability of success at each trial is p and probability of failure is q =1-p. The distribution can be given as follows 
782_negative binomial distribution.png 
The mean, skewness, variance, and kurtosis of the distribution are as follows:
806_negative binomial distribution1.png 
Often used to model over the dispersion in count data.  

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