# Poisson distribution (chart) Calculator

## Calculates a table of the probability mass function, or lower or upper cumulative distribution function of the Poisson distribution, and draws the chart.

 select function probability mass flower cumulative distribution Pupper cumulative distribution Q mean λ λ≧0 [ initial percentile x x=0,1,2,.. increment repetition ]
 $\normal Poisson\ distribution\\[10](1)\ probability\ mass\\\hspace{30}f(x,\lambda)={\large\frac{e^{-\lambda}\lambda^x}{\Gamma(x+1)}}\\(2)\ lower\ cumulative\ distribution\\\hspace{30}P(x,\lambda)={\large\sum_{t=0}^{x}}f(t,\lambda)\\(3)\ upper\ cumulative\ distribution\\\hspace{30}Q(x,\lambda)={\large\sum_{t=x}^{\infty}}f(t,\lambda)\\$

Poisson distribution (chart)
 [1-7] /7 Disp-Num5103050100200
[1]  2019/02/08 09:23   Male / 50 years old level / Self-employed people / Useful /
Purpose of use
Modeling of sales on a SaaS website
[2]  2017/12/14 06:42   Male / 30 years old level / A teacher / A researcher / Useful /
Purpose of use
What volume should be taken from a suspension of single cells to ensure that only 0 or 1 cell are present in each draw.
[3]  2017/07/26 11:07   Male / 50 years old level / A retired people / Very /
Purpose of use
Explore the distribution of queueing delay when a router that features a rate-limiter sends packets out towards a modem. I assume that the egress queue that the router has has a certain buffer capacity of n _packets_ max (estimate = 16) rather than counting total bytes (in any case, in the scenario in question we can assume that all Tx packets are fixed length, at the interface maximum in fact). If the mean queue length is m packets, how often will the buffer overflow i.e. q_len(t) > 16, and how often will the modem possibly be temporarily idle for a short time because the interval between arrival times of packets is too long? Would that be q_len(t) < 1? Looking at the cumulative distributions for this.
Comment/Request
It would be nice to have an option to see the two cumulative functions at the same time side-by-side, and possibly also the probability mass function as well, without needing to switch back and forward.
[4]  2015/03/23 08:00   Male / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
visualizing the distributions used for our statistics classes
[5]  2013/11/22 06:50   Male / 50 years old level / An engineer / Very /
Purpose of use
If I'm a health insurer under Obamacare and I an average of 2 of my 100 customers get expensively ill each year, what is the probability that 4 or more people will get sick and a given year and bankrupt me if my premiums aren't high enough?
[6]  2012/06/05 23:26   Male / 20 years old level / An office worker / A public employee / Very /
Purpose of use
To determine the probability of receiving different levels of orders in a fixed period of time. This will allow us to determine how much we need to increase capacity in order to meet demand.
[7]  2009/03/04 14:00   Male / 20 level / A university student / Very /
Purpose of use
Statistics Assignment
Comment/Request
Good

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