poisson

I'm attempting to write my own function to understand how the Poisson distribution behaves within a Maximum Likelihood Estimation framework (as it applies to GLM). I'm familiar with R's handy glm function, but wanted to try and hand-roll some code to understand what's going on: n <- 10000 # sample size b0 <- 1.0 # intercept b1 <- 0.2 # coefficient x <- runif(n=n, min=0, max=1.5) # generate covariate values lp <- b0+b1*x # linear predictor lambda <- exp(lp) # compute lamda y <- rpois(n=n, lambda=lambda) # generate y-values dta <- data.frame(y=y, x=x) # generate dataset negloglike <- function

I want to define my own density function to be used in the formula call to mle2 from R 's bbmle package. The parameters of the model are estimated but I cannot apply functions like residuals or predict on the returned mle2 object. This is an example in which I define a function for a simple Poisson model. library(bbmle) set.seed(1) hpoisson <- rpois(1000, 10) myf <- function(x, lambda, log = FALSE) { pmf <- (lambda^x)*exp(-lambda)/factorial(x) if (log) log(pmf) else pmf } myfit <- mle2(hpoisson ~ myf(lambda), start = list(lambda=9), data=data.frame(hpoisson)) residuals(myfit) In myfit , the

I would like to plot the density function of a Poisson distribution. I am not sure why I get a jaggy line (in blue). On the sample plot, the normal density curve (in red) looks smooth. It is because the reason the Poisson density function doesn't accept decimal values? How to eliminate the zigzag in the Poisson density plot? Thanks very much for any help. library(ggplot2) ggplot(data.frame(X = seq(5, 30)), aes(x = X)) + stat_function(fun=dpois, geom="line", size=2, color="blue3", args = list(lambda = 15)) + stat_function(fun=dnorm, geom="line", size=2, color="red4", args = list(mean=20, sd=2))

I read somewhere that the python library function random.expovariate produces intervals equivalent to Poisson Process events. Is that really the case or should I impose some other function on the results? On a strict reading of your question, yes, that is what random.expovariate does. expovariate gives you random floating point numbers, exponentialy distributed. In a Poission process the size of the interval between consecutive events is exponential. However, there are two other ways I could imagine modelling poisson processes Just generate random numbers, uniformly distributed and sort them.