Simple Interactive Statistical Analysis
Negative Binomial III
Input.
Input for the mean or average "Expected" can be a proportion with a real between '0' (zero) and '1' (one). It can also be the expected mean with a real value one or above. Input for the number "Selected" box must be a real larger than -1. For the "non selected" box, must be a positive integer value.
Explanation.
This version of the negative binomial gives the probability of sampling k=0,1,2,…etc "green" after you have sampled "r" "reds". Say, the population consists of an Expected proportion of "p" red and "1-p" green. You sample randomly from this population and stop when you have r=10 reds. What is the probability of also having k=0,1,2,3 greens in your sample? This question is answered by this version of the Negative Binomial Distribution.
The Geometric Distribution is a special case of this negative binomial distribution with the number selected, in the second blue box, being '1' (one).
Zero Truncated Negative Binomial.
The zero truncated Negative Binomial distribution concerns a Negative Binomial distribution without zeros. Please consult the z.t.poisson and the Binomial help page for more information.
Note that in the zero truncated negative binomial distribution the relationship between the proportion and the distribution mean is different and considerably more complex than in the usual Negative Binomial procedure. If you input the mean expected count the program will echo the expected proportion. The mean should have a value above one. The mean can also be entered as a proportion The proportion should have a value above zero.
Special cases of the the zero truncated negative binomial distribution are the "extended truncated negative binomial distribution": with the parameter "selected" having a value between -1 and zero (0) (try it); and the "zero truncated geometric distribution": with the value in the selected box being one (1).
