DistributionView

The DistributionView software is a simulator that works by writing mathematical expressions width distributions. It allows graphic visualization of series, histograms and scatterplots, and have easy import/export of data.

The generator COM object of DistributionView, the LOR.Distribution, can also be executed in any environment that allows creation of COM objects. Click here to get a sample Excel file running the generator. See the code in the end of this file with the Excel example, and also an example for use in MatLab.

The most recent version of this page is located at http://jcoelho.m6.net/freeware/DistributionView.html, and the instalation file can be downloaded at http://jcoelho.m6.net/freeware/DistributionView.msi (Version 2.3, 2004/07/10, 4.27Mb). An engine (command line program), that work with EngineTester (http://www.univ-ab.pt/~jcoelho/EngineTester.html), can be downloaded at http://jcoelho.m6.net/freeware/DistributionEngine.zip. This software is freeware, you can use it for any propose, if this page is refered. Contact email: jcoelho@univ-ab.pt.

Old versions: http://jcoelho.m6.net/freeware/DistributionView_2_21.msi (Version 2.21, 2005/03/02, 1.09Mb)

Distribution List

Continuous Distributions

Distribution

Arguments

Comments

Uniform min; max returns a value between min and max, with equal probability

Exponential mean
returns a value of a exponential distribution. If a set of values was generated by a uniform distribution, the difference between consecutive values, follow an exponential distribution.

Normal mean; dev. returns a value of a normal distribution. These distributions are very common because a sum of several independent random variables of any distribution, is a normal distribution.

Lognormal mean; mode; min returns a value of a lognormal distribution. These distributions are common because a product of several independent random variables of any distribution, is a lognormal distribution.

Triangular min; mode; max returns a value of a triangular distribution. Is a distribution with a simple density function (a triangle), easy to explain in a non-statistic environment.

Chi_square degree returns a value of a sum of "degree" N(0;1)^2 distributions

t_student degree returns a value of N(0;1)/sqrt(CHI2(degree)/degree)

F_distribution d1; d2 returns a value of (CHI2(d1)/d1)/(CHI2(d2)/d2)

Cauchy location; scale returns a value of a Cauchy distribution.

Fisher_Tippett (extreme value) a; b returns a value of a Fisher-Tippett distribution

Laplace (double exponential) a returns a value of E(a)-E(a)

Logistic location; scale returns a value of a Logistic distribution

Pareto a; b returns a value of a Pareto distribution

Weibull a; b returns a value of a Weibull distribution

Discrete Distributions

Distribution

Arguments

Comments

Binomial N; p returns the number of success in N experiences with p probability of success

Geometric p returns the number of failures until the first success are archived in experiences with p probability of success

Negative_Binomial r; p returns the number of failures until r success are archived in experiences with p probability of success

Hipergeometric Mp; Mq; N returns the number good elements in a random size N sample of a set with Mp good elements and Mq bad elements

Poisson mean returns the number of events per time unit

RND (random) x1;x2;...;xn returns one of x1;...;xn

Function List

Function

Arguments

Comments

max x1;x2;...;xn returns the maximal value of x1;...;xn

min x1;x2;...;xn returns the minimal value of x1;...;xn

sum x1;x2;...;xn returns the sum of x1;...;xn

mul x1;x2;...;xn returns the product of x1;...;xn

div x1;x2 returns x1/x2

pow x1;x2 returns x1^x2

if x1;x2;x3 returns x2 if x1>0, otherwise returns x3

cond u;p1;d1;...;pn;dn The first distribution (u) is executed, and also the distributions p (p1,...,pn), subtracting the value returned by u. When this value is negative, in p3 for instance, d3 is returned. If u=[Uniform 0 1], then pi is the probability of di to be returned.

set v1;d1;...;vn;dn
Allows assigning distributions (d1) to variables (v1), and returns the last distribution (dn). Note that d2 can use v1, and d3 can use v1 and v2, and so on, allowing generation of dependent random variables.

sin; sinh; asin x returns the sines, hyperbolic sines and arcsine (angles in radians).

cos; cosh; acos x returns the cosines, hyperbolic cosines and arccosine.

tan; tanh; atan x returns the tangent, hyperbolic tangent and arctangent.

ceil, abs x returns the smallest integer that is greater than or equal to x and the absolute value of x

exp; log; log10 x returns the exponential value, natural logarithm and base 10 logarithm

sqrt x returns the square root

lt x1; x2 returns x1<x2

gt x1; x2 returns x1>x2

elt x1; x2 returns x1<=x2

egt x1; x2 returns x1>=x2

eq x1;...;xn returnsx1=...=xn

or x1;...;xn returns x1||...||xn

and x1;...;xn returns x1&&...&&xn

not x returns !x

+ * / ^ <= >= < > = || && - are binary operators to SUM; MUL; DIV; POW; ELT; EGT; LT; GT; EQ; OR; AND. Example: "a*b" will expand to "[mul a b]"

Constant List

Constant

Value

Comments

PI 3.14159265 the ratio of the circumference of a circle to its diameter

EULER 2.718281828 The base of the natural logarithm

Examples

List sintax

Function sintax

Comments

[Normal 0 1] Normal(0;1) Normal distribution, with mean 0 and standard deviation 1

[Exponential 10] Exponential(10) Exponential distribution, with mean 10

[rnd 1 2 3 4 5 6] rnd(1 2 3 4 5 6) Generation of 1 value between 6

[sum [rnd 1 2 3 4 5 6] [rnd 1 2 3 4 5 6]] rnd(1 2 3 4 5 6)+rnd(1 2 3 4 5 6) Generation of a sum of two values from 1 to 6

[set DADOS [sum [rnd 1 2 3 4 5 6] [rnd 1 2 3 4 5 6]] [or [eq DADOS 7] [eq DADOS 11]]] set(DADOS sum(rnd(1 2 3 4 5 6) rnd(1 2 3 4 5 6)) or(DADOS=7 DADOS=11)
Generation of two value from 1 to 6, and two variables where one is the sum of the two values and other is 1 if the sum is 7 or 11, and 0 otherwise.

[set Normal [Normal 0 1] Triangular [Triangular -1 0 1] Uniform [Uniform -1 1]] set(Normal Normal(0 1) Triangular Triangular(-1 0 1) Uniform Uniform(-1 1)) Three variables/distribuitions, a Normal, a Triangular and an Uniform distribution

[cond [Uniform 0 100] 10 0 15 1 5 2 30 3 20 4 20 5] cond(Uniform(0 100) 10 0 15 1 5 2 30 3 20 4 20 5) A conditional distribution, generating discrete values: 0 (with 10%); 1 (15%); 2 (5%); 3 (30%); 4 (20%) 5 (20%)

[set exp [Exponential 10] max [max [Exponential 10] [Exponential 10]]] set(exp Exponential(10) max max(Exponential(10) Exponential(10))) A exponential distribution with mean 10, and the max of two exponential distributions of mean 10

[sum [Exponential 10] [div [mul [Normal 0 1] [Normal 0 1]] [Uniform 1 2]]] Exponential(10)+Normal(0 1)*Normal(0 1)/Uniform(1 2) Expression envolving different distributions

[set pow [pow [Normal 0 1] 2] mul [mul [Normal 0 1] [Normal 0 1]]] set(pow Normal(0 1)^2 mul Normal(0 1)*Normal(0 1))
The square of normal distribution, and the product of two normal distributions

[cond [Uniform 0 100] 40 [Normal 10 1] 60 [Normal 15 2]] cond(Uniform(0 100) 40 Normal(10 1) 60 Normal(15 2))
Returns Normal(10 1) with 40% chance, and Normal(15 2) with 60% chance

[set DA [Normal 10 1] [max [sum [Normal 10 1] DA] [sum [Normal 10 1] [max DA [Normal 10 1]]]]] set(DA Normal(10 1) max(Normal(10 1)+DA Normal(10 1)+max(DA Normal(10 1))))
Generation of a variable Normal(10 1) and other variable with some dependencies

[set V1 [pow [Normal 0 1] 3] V2 [sum -10 [Exponential 10]]] set(V1 Normal(0 1)^3 V2 -10+Exponential(10))
Generation of two variables not independent

VB Code to run LOR.Distribution

This code runs in VBA, and only needs the LOR.DLL file registered in the system, that is done by installing the DistributionView:

Dim dist As Object

Set dist = CreateObject("LOR.Distribution")

dist.seed = 1 ' set seed number

dist.Definition = "Normal(0;1)"

For Each x In Selection

dist.NextValue

x.Value = dist.Value

MatLAb Code to run LOR.Distribution

This code runs in a distribution.m file, and only needs the LOR.DLL file registered in the system, that is done by installing the DistributionView:

function dist = distribution(definition)
% This function returns a function that use a COM object (LOR.Distribution)
% to generate distributions acoording to definition 
% (see http://jcoelho.m6.net/freeware/DistributionView.html)

hCom=actxserver('LOR.Distribution');

hCom.Definition=definition;

dist=@f;

    function v=f(x)
        if nargin==1, hCom.Seed=x; end
        hCom.NextValue();
        v=hCom.Value;
    end
end

This function returns a generator for the definition given. For instance, you can do things like:

c=distribution('Exponential(10)');

d=distribution('Max(Exponential(10);Normal(10;1))');

c() % returns a value that follows the distribution c

c(1); d(1); % resets seed number generator to 1, to allow re-generate the same values later

for k=1:100; p(k)=c(); end; % put 100 values in p, following the distribution c

for k=1:100; q(k)=d(); end; % put 100 values in q, following the distribution d

R Code to run LOR.Distribution

To install R go to http://www.r-project.org/. The following code require that you install the library RDCOMClient for R, available in http://www.omegahat.org/RDCOMClient/.

library(RDCOMClient)
dist=COMCreate("LOR.Distribution")
dist[["Definition"]]="Normal(0;1)"
dist[["Seed"]]=1
Generate<-function() {
  dist$NextValue()
  dist$Value()
}

The function Generate will return values acording to the distribution.

Last change on 2006-04-04

Distribution	Arguments	Comments
Uniform	min; max	returns a value between min and max, with equal probability
Exponential	mean	returns a value of a exponential distribution. If a set of values was generated by a uniform distribution, the difference between consecutive values, follow an exponential distribution.
Normal	mean; dev.	returns a value of a normal distribution. These distributions are very common because a sum of several independent random variables of any distribution, is a normal distribution.
Lognormal	mean; mode; min	returns a value of a lognormal distribution. These distributions are common because a product of several independent random variables of any distribution, is a lognormal distribution.
Triangular	min; mode; max	returns a value of a triangular distribution. Is a distribution with a simple density function (a triangle), easy to explain in a non-statistic environment.
Chi_square	degree	returns a value of a sum of "degree" N(0;1)^2 distributions
t_student	degree	returns a value of N(0;1)/sqrt(CHI2(degree)/degree)
F_distribution	d1; d2	returns a value of (CHI2(d1)/d1)/(CHI2(d2)/d2)
Cauchy	location; scale	returns a value of a Cauchy distribution.
Fisher_Tippett (extreme value)	a; b	returns a value of a Fisher-Tippett distribution
Laplace (double exponential)	a	returns a value of E(a)-E(a)
Logistic	location; scale	returns a value of a Logistic distribution
Pareto	a; b	returns a value of a Pareto distribution
Weibull	a; b	returns a value of a Weibull distribution

Function	Arguments	Comments
max	x1;x2;...;xn	returns the maximal value of x1;...;xn
min	x1;x2;...;xn	returns the minimal value of x1;...;xn
sum	x1;x2;...;xn	returns the sum of x1;...;xn
mul	x1;x2;...;xn	returns the product of x1;...;xn
div	x1;x2	returns x1/x2
pow	x1;x2	returns x1^x2
if	x1;x2;x3	returns x2 if x1>0, otherwise returns x3
cond	u;p1;d1;...;pn;dn	The first distribution (u) is executed, and also the distributions p (p1,...,pn), subtracting the value returned by u. When this value is negative, in p3 for instance, d3 is returned. If u=[Uniform 0 1], then pi is the probability of di to be returned.
set	v1;d1;...;vn;dn	Allows assigning distributions (d1) to variables (v1), and returns the last distribution (dn). Note that d2 can use v1, and d3 can use v1 and v2, and so on, allowing generation of dependent random variables.
sin; sinh; asin	x	returns the sines, hyperbolic sines and arcsine (angles in radians).
cos; cosh; acos	x	returns the cosines, hyperbolic cosines and arccosine.
tan; tanh; atan	x	returns the tangent, hyperbolic tangent and arctangent.
ceil, abs	x	returns the smallest integer that is greater than or equal to x and the absolute value of x
exp; log; log10	x	returns the exponential value, natural logarithm and base 10 logarithm
sqrt	x	returns the square root
lt	x1; x2	returns x1<x2
gt	x1; x2	returns x1>x2
elt	x1; x2	returns x1<=x2
egt	x1; x2	returns x1>=x2
eq	x1;...;xn	returnsx1=...=xn
or	x1;...;xn	returns x1\|\|...\|\|xn
and	x1;...;xn	returns x1&&...&&xn
not	x	returns !x
+ * / ^ <= >= < > = \|\| &&	-	are binary operators to SUM; MUL; DIV; POW; ELT; EGT; LT; GT; EQ; OR; AND. Example: "a*b" will expand to "[mul a b]"

Constant	Value	Comments
PI	3.14159265	the ratio of the circumference of a circle to its diameter
EULER	2.718281828	The base of the natural logarithm

List sintax	Function sintax	Comments
[Normal 0 1]	Normal(0;1)	Normal distribution, with mean 0 and standard deviation 1
[Exponential 10]	Exponential(10)	Exponential distribution, with mean 10
[rnd 1 2 3 4 5 6]	rnd(1 2 3 4 5 6)	Generation of 1 value between 6
[sum [rnd 1 2 3 4 5 6] [rnd 1 2 3 4 5 6]]	rnd(1 2 3 4 5 6)+rnd(1 2 3 4 5 6)	Generation of a sum of two values from 1 to 6
[set DADOS [sum [rnd 1 2 3 4 5 6] [rnd 1 2 3 4 5 6]] [or [eq DADOS 7] [eq DADOS 11]]]	set(DADOS sum(rnd(1 2 3 4 5 6) rnd(1 2 3 4 5 6)) or(DADOS=7 DADOS=11)	Generation of two value from 1 to 6, and two variables where one is the sum of the two values and other is 1 if the sum is 7 or 11, and 0 otherwise.
[set Normal [Normal 0 1] Triangular [Triangular -1 0 1] Uniform [Uniform -1 1]]	set(Normal Normal(0 1) Triangular Triangular(-1 0 1) Uniform Uniform(-1 1))	Three variables/distribuitions, a Normal, a Triangular and an Uniform distribution
[cond [Uniform 0 100] 10 0 15 1 5 2 30 3 20 4 20 5]	cond(Uniform(0 100) 10 0 15 1 5 2 30 3 20 4 20 5)	A conditional distribution, generating discrete values: 0 (with 10%); 1 (15%); 2 (5%); 3 (30%); 4 (20%) 5 (20%)
[set exp [Exponential 10] max [max [Exponential 10] [Exponential 10]]]	set(exp Exponential(10) max max(Exponential(10) Exponential(10)))	A exponential distribution with mean 10, and the max of two exponential distributions of mean 10
[sum [Exponential 10] [div [mul [Normal 0 1] [Normal 0 1]] [Uniform 1 2]]]	Exponential(10)+Normal(0 1)*Normal(0 1)/Uniform(1 2)	Expression envolving different distributions
[set pow [pow [Normal 0 1] 2] mul [mul [Normal 0 1] [Normal 0 1]]]	set(pow Normal(0 1)^2 mul Normal(0 1)*Normal(0 1))	The square of normal distribution, and the product of two normal distributions
[cond [Uniform 0 100] 40 [Normal 10 1] 60 [Normal 15 2]]	cond(Uniform(0 100) 40 Normal(10 1) 60 Normal(15 2))	Returns Normal(10 1) with 40% chance, and Normal(15 2) with 60% chance
[set DA [Normal 10 1] [max [sum [Normal 10 1] DA] [sum [Normal 10 1] [max DA [Normal 10 1]]]]]	set(DA Normal(10 1) max(Normal(10 1)+DA Normal(10 1)+max(DA Normal(10 1))))	Generation of a variable Normal(10 1) and other variable with some dependencies
[set V1 [pow [Normal 0 1] 3] V2 [sum -10 [Exponential 10]]]	set(V1 Normal(0 1)^3 V2 -10+Exponential(10))	Generation of two variables not independent