User talk:Swachira

Welcome to Wiki Course Notes! We hope you will contribute much and well. You will probably want to read the help pages. Again, welcome and have fun! WikiSysop 20:30, 8 May 2013 (MDT)

Thursday 9th May 2013 Summary

Sampling methods: 1. Multiplicative Congruential Algorithm This is algorithm involves three integer parameters; a, b and m, and an initial value x, known as the seed. A sequence of numbers is defined by x_k+1 = ax_k + b mod m where mod m means take the remainder after division by m. Therefore the random values are between 0 and m inclusive. To normalize the values, we divide by m-1, resulting in numbers uniformly distributed in the interval [0, 1].

2.Inverse Transform Method We use this method when we want to see a certain trend in our random values, such as an exponential trend. The steps involved in this algorithm include: Step 1: Take U~U[0,1]

Step 2: Define X = F^-1(U) Where F(x) = P(X<=x) (the cdf of the distribution we wish to map our random data)

     F-1(.) denotes the function inverse of F(.)

Therefore F(X)= P(X<=x)

   = P(F-1(U) <= x)
   = P(F(F-1(U) <= F(x))
   = P(U<= F(x))