Simulations and programming in R

1
Simulations and programming in R
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Why to simulate and program in R at all?

• ADVANTAGES
• All R facilities can be used in the simulations
• Random number generators
• Handy way of creating own R-functions
• Simulation results are readily in R to be
  visualized and analyzed
• DISADVANTAGES
• Loops may be slow
• Writing output may be slower than e.g. in C
  language
• "Black-horse" solution
• Compile C-code under R

3
Random numbers

• Random numbers are numbers drawn from a specific
  probability distribution

Area of a bar approximates the probability of
getting a number in that interval. These
probabilities sum up to one.
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Most common distributions

• CONTINUOUS
• Normal distribution e.g. weight and length of an
  individual
• Exponential distribution 'waiting time', e.g.
  lifetime of an individual
• Uniform distribution flat distribution, i.e.
  values do not concentrate around some peak but
  are spread randomly
• DISCRETE
• Poisson distribution number count, e.g. number
  of fish caught
• Binomial outcome of tossing coin, choice to
  metamorphose or not
• (Multinomial same as binomial except more than
  two possible outcomes)

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Random number generators

• Random number tools for normal distribution
• rnorm() random number generator
• dnorm() density function (probability function
  for discrete distributions)
• pnorm() distribution function
• qnorm() quantile function
• Similarly for binomial, Poisson, exponential,
  multinomial, uniform distributions (and many
  others), e.g.
• runif(), rexp(), rpois(), rbinom()
• -gt DEMO 1

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Creating an R-function

• Name of the function function( input
  parameters )

Procedures to be carried out
All the input stuff needed for the procedures the
function will perform
DEMO 2
7
Basic programming loops in R

• Much of simulations is based on three loops
• for( index in index vector )
• Repeats the procedure for all the indices
• while( a logical condition )
• Repeats the procedure until the logical
  conditions is FALSE
• if ( a logical condition ) else
• If the condition holds, does the first procedure,
  otherwise the second.

DEMO 3