Using Python 2.x, generate random samples from the Poisson distribution with = 4

Question

Using Python 2.x, generate random samples from the Poisson distribution with = 4, using 20, 50, 100, 200, 500, 1000, 2000 data points. For each of the sample, estimate the mean and standard deviation. Then plot the estimated values as functions of the sample size.

2) For each of the sample generated, estimate the 95% confidence interval of the estimated mean. Plot of the upper and lower bound of the confidence intervals as function of the sample size. How often does the true parameter value fall outside of the confidence intervals?

Explanation / Answer

init: Let L exp(), k 0 and p 1. do: k k + 1. Generate uniform random number u in [0,1] and let p p × u. while p > L. return k 1. int c beta = PI/sqrt(4.0*lambda) alpha = beta*lambda k = log(c) - lambda - log(beta) forever { u = random() x = (alpha - log((1.0 - u)/u))/beta n = floor(x + 0.95) if (n < 0) continue v = random() y = alpha - beta*x lhs = y + log(v/(1.0 + exp(y))^2) rhs = k + n*log(lambda) - log(n!) if (lhs

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