Obtaining a Uniform Random Number Generator
Some form of a uniform random number generator, called a pseudorandom num-
ber generator and abbreviated (PRNG), can usually be found as an intrinsic function
within many of the more popular computer programming languages. If the computer
language you are using does not have a uniform random number generator, then you
can obtain one from off the internet. Pseudorandom number generators generate a
sequence of numbers {xn}satisfying 0 ≤xn≤ 1. The sequence of numbers generated
is not truly random because of technical issues involving the mathematical methods
used to generate the uniform random numbers. Most of the PRNG programs in use
have passed many statistical tests which guarantee that the sequence generated is
random enough for Monte Carlo studies and other statistical applications.
Linear Interpolation
In obtaining a specific numerical value from a table of (x, y )values it is sometimes
necessary to use linear interpolation where a line is constructed between two known
numerical values and then values along the line are used as estimates for the tabular
values between the known values. In one dimension, one can say that if (x 1 , y 1 )and
(x 2 , y 2 )are known values, then if xis a value between x 1 and x 2 , the corresponding
value for y is given by y =y 1 +
(y
2 −y 1
x 2 −x 1
)
(x−x 1 ). This result can be expressed in a
variety of forms. One form is to make the substitution x 2 −x 1 =hwith x=x 1 +βh ,
then y=y 1 +β(y 2 −y 1 )or y= (1 −β)y 1 +βy 2.
Interpolation in two-dimension
Consider the set of values in a table as illus-
trated in the accompanying figure. Let F 11
denote the value in the table corresponding
to the position (x 1 , y 1 ). Similarly, define the
values F 12 , F 21 and F 22 corresponding respec-
tively to the points (x 1 , y 2 ),(x 2 , y 1 )and (x 2 , y 2 ).
Interpolation over this two dimensional ar-
ray is the problem of determining the values
Fα,Fβ and Fα,β which are positioned on the
boundaries and interior to the box connect-
ing the known data values F 11 , F 12 , F 22 , F 21.
