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Different texts (and even different parts of this article) adopt slightly different definitions for the negative binomial distribution. They can be distinguished by whether the support starts at k = 0 or at k = r, whether p denotes the probability of a success or of a failure, and whether r represents success or failure, [1] so identifying the specific parametrization used is crucial in any ...
For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule.
Therefore, the Poisson distribution with parameter λ = np can be used as an approximation to B(n, p) of the binomial distribution if n is sufficiently large and p is sufficiently small. According to rules of thumb, this approximation is good if n ≥ 20 and p ≤ 0.05 [ 36 ] such that np ≤ 1 , or if n > 50 and p < 0.1 such that np < 5 , [ 37 ...
The multinomial distribution, a generalization of the binomial distribution. The multivariate normal distribution, a generalization of the normal distribution. The multivariate t-distribution, a generalization of the Student's t-distribution. The negative multinomial distribution, a generalization of the negative binomial distribution.
Negative excess kurtosis indicates a platykurtic distribution, which doesn’t necessarily have a flat top but produces fewer or less extreme outliers than the normal distribution. For instance, the uniform distribution (ie one that is uniformly finite over some bound and zero elsewhere) is platykurtic. On the other hand, positive excess ...
A simple example illustrating these relationships is the binomial distribution with n = 10 and p = 0.09. [35] This distribution when plotted has a long right tail. The mean (0.9) is to the left of the median (1) but the skew (0.906) as defined by the third standardized moment is positive. In contrast the nonparametric skew is -0.110.
Different texts (and even different parts of this article) adopt slightly different definitions for the negative binomial distribution. They can be distinguished by whether the support starts at k = 0 or at k = r, whether p denotes the probability of a success or of a failure, and whether r represents success or failure, [1] so identifying the specific parametrization used is crucial in any ...
This is because the negative binomial distribution can be derived from a Poisson-stopped sum of logarithmic random variables. [11]: 606–607 The decimal digits of the geometrically distributed random variable Y are a sequence of independent (and not identically distributed) random variables.