montecarlo

For large n (see below for how to determine what's large enough), it's safe to treat, by the central limit theorem, the distribution of the sample mean as normal (gaussian) but I'd like a procedure that gives a confidence interval for any n . The way to do that is to use a Student T distribution with n-1 degrees of freedom. So the question is, given a stream of data points that you collect or encounter one at a time, how do you compute a c (eg, c=.95 ) confidence interval on the mean of the data points (without storing all of the previously encountered data)? Another way to ask this is: How do

Suppose I would like to calculate Pi with Monte Carlo simulation as an exercise. I am writing a function, which picks a point in a square (0, 1), (1, 0) at random and tests if the point is inside the circle. import scala.math._ import scala.util.Random def circleTest() = { val (x, y) = (Random.nextDouble, Random.nextDouble) sqrt(x*x + y*y) <= 1 } Then I am writing a function, which takes as arguments the test function and the number of trials and returns the fraction of the trials in which the test was found to be true. def monteCarlo(trials: Int, test: () => Boolean) = (1 to trials).map(_ =>

I need a pseudo random number generator for 2D Monte Carlo simulation that doesn't have the characteristic hyperplanes that you get with simple LCGs. I tested the random number generator Rnd() in Excel 2013 using the following code (takes about 5 secs to run): Sub ZoomRNG() Randomize For i = 1 To 1000 Found = False Do x = Rnd() ' 2 random numbers between 0.0 and 1.0 y = Rnd() If ((x > 0.5) And (x < 0.51)) Then If ((y > 0.5) And (y < 0.51)) Then ' Write if both x & y in a narrow range Cells(i, 1) = i Cells(i, 2) = x Cells(i, 3) = y Found = True End If End If Loop While (Not Found) Next i End

I am using R to construct an agent based model with a monte carlo process. This means I got many functions that use a random engine of some kind. In order to get reproducible results, I must fix the seed. But, as far as I understand, I must set the seed before every random draw or sample. This is a real pain in the neck. Is there a way to fix the seed? set.seed(123) print(sample(1:10,3)) # [1] 3 8 4 print(sample(1:10,3)) # [1] 9 10 1 set.seed(123) print(sample(1:10,3)) # [1] 3 8 4 There are several options, depending on your exact needs. I suspect the first option, the simplest is not

Here's a MWE of a much larger code I'm using. Basically, it performs a Monte Carlo integration over a KDE ( kernel density estimate ) for all values located below a certain threshold (the integration method was suggested over at this question BTW: Integrate 2D kernel density estimate ). import numpy as np from scipy import stats import time # Generate some random two-dimensional data: def measure(n): "Measurement model, return two coupled measurements." m1 = np.random.normal(size=n) m2 = np.random.normal(scale=0.5, size=n) return m1+m2, m1-m2 # Get data. m1, m2 = measure(20000) # Define limits