Skip to main content
Tweeted twitter.com/#!/StackStats/status/521969180355362817
Made title more searchable, capitalization
Source Link
Glen_b
  • 290.5k
  • 37
  • 652
  • 1.1k

Finding Find the expected value fromparameter of a Poisson, given the poisson cdfdistribution function at a known value

Assuming a poissonPoisson distribution, the probability ($\alpha$) that the result will fall within the range $0\ldots k$ is given by the following expression:

\begin{equation} \alpha = e^{-\lambda}\sum_{i=0}^{k}\frac{\lambda^i}{i!} \end{equation}

where $\lambda$ is the expected value (and variance).

In this particular case, the probability ($\alpha$) as well as the range ($k$) is known but the expected value ($\lambda$) is unknown. Is there a analytical solution or close approximation to the value of $\lambda$?

I have so far been solving the problem numerically by minimizing the equation but this is consuming a rather large part of the processing time of my computer which is why I am looking for ways to optimize my code.

Finding the expected value from the poisson cdf

Assuming a poisson distribution, the probability ($\alpha$) that the result will fall within the range $0\ldots k$ is given by the following expression:

\begin{equation} \alpha = e^{-\lambda}\sum_{i=0}^{k}\frac{\lambda^i}{i!} \end{equation}

where $\lambda$ is the expected value (and variance).

In this particular case, the probability ($\alpha$) as well as the range ($k$) is known but the expected value ($\lambda$) is unknown. Is there a analytical solution or close approximation to the value of $\lambda$?

I have so far been solving the problem numerically by minimizing the equation but this is consuming a rather large part of the processing time of my computer which is why I am looking for ways to optimize my code.

Find the parameter of a Poisson, given the distribution function at a known value

Assuming a Poisson distribution, the probability ($\alpha$) that the result will fall within the range $0\ldots k$ is given by the following expression:

\begin{equation} \alpha = e^{-\lambda}\sum_{i=0}^{k}\frac{\lambda^i}{i!} \end{equation}

where $\lambda$ is the expected value (and variance).

In this particular case, the probability ($\alpha$) as well as the range ($k$) is known but the expected value ($\lambda$) is unknown. Is there a analytical solution or close approximation to the value of $\lambda$?

I have so far been solving the problem numerically by minimizing the equation but this is consuming a rather large part of the processing time of my computer which is why I am looking for ways to optimize my code.

Source Link

Finding the expected value from the poisson cdf

Assuming a poisson distribution, the probability ($\alpha$) that the result will fall within the range $0\ldots k$ is given by the following expression:

\begin{equation} \alpha = e^{-\lambda}\sum_{i=0}^{k}\frac{\lambda^i}{i!} \end{equation}

where $\lambda$ is the expected value (and variance).

In this particular case, the probability ($\alpha$) as well as the range ($k$) is known but the expected value ($\lambda$) is unknown. Is there a analytical solution or close approximation to the value of $\lambda$?

I have so far been solving the problem numerically by minimizing the equation but this is consuming a rather large part of the processing time of my computer which is why I am looking for ways to optimize my code.