In this section we will study a family of distributions that has special importance in probability and statistics. In particular, the arrival times in the Poisson process have gamma distributions, and...In this section we will study a family of distributions that has special importance in probability and statistics. In particular, the arrival times in the Poisson process have gamma distributions, and the chi-square distribution in statistics is a special case of the gamma distribution. Also, the gamma distribution is widely used to model physical quantities that take positive values.
In Bernoulli trials, the time of the nth arrival has the negative binomial distribution with parameters n and p (the success probability), while in the Poisson process, as we now kno...In Bernoulli trials, the time of the nth arrival has the negative binomial distribution with parameters n and p (the success probability), while in the Poisson process, as we now know, the time of the nth arrival has the gamma distribution with parameters n and r (the rate).
It calls for values of n and p, selects suitable k values, and plots the distribution function for the binomial, a continuous approximation to the distribution function for the Poisson, an...It calls for values of n and p, selects suitable k values, and plots the distribution function for the binomial, a continuous approximation to the distribution function for the Poisson, and continuity adjusted values of the gaussian distribution function at the integer values.
