/ Erlang.NumberBiasedRands

Instead of a truly random number, you wish to randomly select a value from a set in which some values are more likely than others. For example, you may wish to simulate a normal distribution (i.e., a "bell curve") for a set of data.

We will give a recipe for generating numbers with a normal distribution (aka Gaussian distribution, the bell shaped one). A library is under way see: Schemathics CVS, but we will discuss a do-it-yourself method for explanatory purposes.

You will have to determine what kind of distribution you want, and locate the appropriate algorithm from a statistics reference.

For this recipe, we will consider the normal (Gaussian) distribution. If you need other distributions see either the CVS or consult a numerical analyst.

The function `make-normal-distributed-variable`

returns a stochastic variable (a thunk) with mean `mu`

and standard deviance `sigma`

.:
500 Can't connect to 127.0.0.1:8778 (connect: Connection refused)

An example of usage: 500 Can't connect to 127.0.0.1:8778 (connect: Connection refused)

If you are unsatisfied with the fact that you get the same numbers as I above, then randomize the source of the random numbers: 500 Can't connect to 127.0.0.1:8778 (connect: Connection refused)

The algorithm used is the polar Box Muller method. The algorithm takes two independent uniformly distributed random numbers between 0 and 1 (present in the code as `(random-real)`

) and generates two numbers with a mean of my and standard deviation sigma. Note that the method produces two numbers at a time. Since we only need one, the second is saved for later in the variable `next`

.

Note that the Perl Cookbook includes an interesting discussion of converting a set of values (and weights) into a distribution. This should also be converted to Scheme and shown here.

Mathematically-inclined Schemers should also take a good look at Schemathics, which contains these and many other statistical methods.

-- BrentAFulgham - 14 May 2004

-- JensAxelSoegaard - 01 Jun 2004

[TODO: Move the following remarks to another recipe]

If you wish to randomly select from a set of weights and values, convert the weights into a probability distribution, then use the resulting distribution to pick a value.

If you have a list of weights and values you want to randomly pick from, follow this two-step process: First, turn the weights into a probability distribution with weight_to_dist below, and then use the distribution to randomly pick a value with weighted_rand:

-- BrentAFulgham - 25 Aug 2004

CookbookForm | |
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TopicType: | Recipe |

ParentTopic: | NumberRecipes |

TopicOrder: | 100 |

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