Pseudo-random number generator

Introduction

To accomplish computational tests about the multi-objective shortest path problem, a generator of random or pseudo-random number is needed. We have used our random generator code (randNet) to produce the instances of this data base. This web page reports some statistical analysis of the pseudo-random numbers obtained with this code. To know more about pseudo-random and true random number you may follow this link: http://www.random.org/essay.html

Theoretical results

Let X, Y and Z be random discrete variables following a discret uniform distribution in the set {1, ..., 100}, then:

P(X = i) = 1/100 = 0.01, ∀ i ∈ {1, ..., 100}
E(X) = 101/2 = 50.5 and V(X) = 9999/12 = 833.25
P(X = Y) = 1/100 = 0.01 and P(X < Y) = P(X > Y) = 99/200 = 0.495
P(X = Y = Z) = 1/10000 = 0.0001 and P(X < Y < Z) = P(X > Y > Z) = 0.1617

Statistical study about the randNet generated values

We consider a sample with 10 000 elements obtained with our code (click here to download the sample file).

Let x_i be i^th value of this sample. Then:

Frequency of i, i ∈ {1, ..., 100}, belongs to the interval [0.0076, 0.0134]

(see the figure in the right hand).

Mean: 49.9463
Standard deviation: 822.5312
Percentage of occurrence:

x_i < x_i+1	x_i = x_i+1	x_i > x_i+1
49.45	1.13	49.42

Percentage of occurrence:

x_i < x_i+1 < x_i+2	x_i = x_i+1 = x_i+2	x_i > x_i+1 >x_i+2
16.12	0.01	16.20

(click on graphic thumbnail to see a large image)

Statistical study about the true random values

We consider a sample with 10 000 elements obtained from http://www.random.org/nform.html

(click here to download the sample file).

Let x_i be i^th value of this sample. Then:

Frequency of i, i ∈ {1, ..., 100}, in the interval [0.0074, 0.0126]
Mean: 50.9537
Standard deviation: 832.2752
Percentage of occurrence:

x_i < x_i+1	x_i = x_i+1	x_i > x_i+1
49.81	1.09	49.10

Percentage of occurrence:

x_i < x_i+1 < x_i+2	x_i = x_i+1 = x_i+2	x_i > x_i+1 >x_i+2
16.89	0.03	16.13

(click on graphic thumbnail to see a large image)