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- https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/05%3A_Special_Distributions/5.08%3A_The_Gamma_DistributionIn 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.
- https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/14%3A_The_Poisson_Process/14.03%3A_The_Gamma_DistributionIn Bernoulli trials, the time of the \( n \)th 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 \( n \)th 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 \( n \)th arrival has the gamma distribution with parameters \( n \) and \( r \) (the rate).
- https://stats.libretexts.org/Bookshelves/Probability_Theory/Applied_Probability_(Pfeiffer)/07%3A_Distribution_and_Density_Functions/7.02%3A_Distribution_ApproximationsIt 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.
