# monte-carlo

1. ### Relative Efficiency

Consider the following equation: T_i = A_i + Z_i * B_i,i=1,2...,6. Suppose for all i(i=1,2,...,6) data generation of A_i and B_i are exactly same for two methods. The two methods differ only in generating data of Z_i. For method 1, Z_i is generated from Bernoulli distribution with...
2. ### Monte Carlo Integration with Computationally expensive Integrant

Consider \mathcal{R}_x = \int_{x'} C(x|x')P(x')dx', where \mathcal{R}_x = risk of following input x C(x|x') = cost of following input x when in fact input x' occured P(x') = known pdf of inputs evaluated for input x' Objective : obtain a decent estimate of the integral Challenge ...
3. ### Improved Monte-Carlo method vs. hit-and-miss method

I am not understanding *Which is more accurate, the hit-and-miss method or the improved Monte-Carlo method?* http://www-stat.stanford.edu/~susan/courses/s208/node14.html it is written that that the hit-and-miss has a higher variance but they showed (variance of improved Monte-Carlo) -...
4. ### Combining probability distribution functions

Hi, I'm comparing different measurement methods. I listed and derived an equation for each error component per measurement method and calculated the probability distribution using the Monte-Carlo method (calculating each error 300.000 times assuming a normal distribution of the input...
5. ### Sampling a hemisphere using an arbitary distribtuion

I am writing a ray tracer and I wish to fire rays from a point **p** into a hemisphere above that point according to some distribution. 1) I have derived a method to uniformly sample within a solid angle (defined by theta) above **p** [1] \phi = 2\pi\xi_1 \alpha = \arccos...
6. ### Fitting distribution - Chi Square Test

Hi, I'm need to test some data for my masterthesis. I'm a newbie to statistics, so please forgive any stupid errors I may have done. I use R for all calculations. I have set of 900000 discrete data points in the range from 1 to 600. I wanna fit a distribution to that data set. I think it is a...