En las simulaciones en las que la suerte influye, son necesarios los números aleatorios. Antes se usaban las tablas de números aleatorios. EN la actualidad, los números aleatorios se suelen obtener con un programa de ordenador. Puesto que estos números se calculan usando una fórmula, no son realmente aleatorios, por lo que se les llama pseudo-aleatorios. Es muy difícil diferenciar los auténticos números aleatorios de los pseudo-aleatorios.
Los números aleatorios deben ser totalmente aleatorios. Deben ser completamente independientes unos de otros y cada número debe tener la misma probabilidad de aparecer.
Los números aleatorios para simular las puntuaciones de un dado, por ejemplo, deben ser números del 1 al 6 y cuando el número de simulaciones es grande el porcentaje de veces que aparece cada número debe ser casi el mismo.
En la generación de números aleatorios se pueden elegir diferentes distribuciones. Los resultados se pueden ver en una tabla o en un gráfico. El valor de los números aleatorios se muestra en una escala vertical. Si el gráfico muestra alguna regularidad, indica que los números no se han generado aleatoriamente.
In simulations where chance plays a role, you need random numbers. In the past, tables were used. Now, random numbers are usually produced by a computer. Because they are calculated using a formula, they are not really random numbers, so they are called pseudo-random numbers. It is very difficult to distinguish between real random numbers and pseudo real numbers.
Random numbers must be totally random. They should be completely independent of each other, and every number should have an equal probability of appearing.
The random numbers for simulating the score on a die, for example, should be whole numbers from 1 to 6 and, with a large number of simulations, the percentage of times each appears should be almost the same.
In the random number generator you can select different distributions. The results can be seen either in a table or a graph. The value of the random number is shown on a vertical scale. If the graph shows any regularity it would indicate that the numbers have not been generated randomly.
Settings and buttons
Settings
In the Settings window you can select a distribution and the accompanying parameters.
Each experiment consists of generating at least one number. However, it is possible to let an experiment consist of generating more than one number. In that case, you have the options to show the mean of that experiment with a small red bar, and to represent the data with a boxplot to obtain an impression of the spread of the numbers generated within an experiment.
Tempo bar
With the tempo bar you can change the speed of the simulation before and during the simulation.
With Step you can track the experiment step by step.
Fast is designed to enable you to create a large quantity of data.
Interrupt/continue
With the space bar you can interrupt or resume the simulation.
clears all results.
saves the results in a file.
sends the results of the simulation direct to Excel. Excel will appear on the taskbar.
Simulation formulas
v1, v2, .. are individual random number variables. In formulas, notation [V1] or [v1] is compulsory.
v put all random variables in one record
Every name is suitable for defining a variable.
Both capitals and lower-case characters can be used.
Examples: altogether = sum(v) or var=Sum(v) or statisGREAT = SUM(V)
count |
values |
var = count(v=6) counts number of sixes var = count((v=3) or (v>5)) counts number of threes and values greater than 5 |
countpar |
number of values in a part |
var = countpart(v=6;1;4) counts number of sixes at variables V1 , .... V4 var = countpart(v=6;5;7) counts number of sixes at 5th , .... 7th variable |
sum |
sum of values |
var=sum(v) computes sum of all values |
sumpart |
sum of part |
var = sumpart(v;4;10) computes sum of V4 , .... V10 |
mean |
mean |
var = mean(v) computes mean of all values |
meanpart |
mean of a part |
var = meanpart(v;4;10) computes mean of V4 , .... V10 |
SD |
standard deviation |
var = SD(v) computes standard deviation of all values |
SDpart |
standard deviation of a part |
var = SDpart(v;4;10) computes standard deviation of V4 , .... V10 |
max |
maximum |
var = max(v) selects maximum value in a record |
min |
minimum |
var = min(v) selects minimum value in a record |
uniquenumbers |
number of different values |
var = uniquenumbers(v) computes number of different values |
med |
median |
var = med(v) computes median of all values |
medpart |
median of a part |
var = medpart(v;4;10) computes median of V4 , .... V10 |
q1 |
first quartile |
var = q1(v) computes first quartile of all values |
q1part |
first quartile of part |
var = q1part(v;4;10) computes first quartile of V4 , .... V10 |
q3 |
third quartile |
var = q3(v) computes third quartile of all values |
q3part |
third quartile of a part |
var = q3part(v;4;10) computes third quartile of V4 , .... V10 |
nvar |
number of variables |
var = nvar(v) computes number of variables |
More possibilities
Summarizing selected variables: var = [v1]+[v2]+[v3]
Linear transformation of all random values and summarize: var = sum(2v+3)