computer simulation & modeling

8/2/2019 Computer Simulation & Modeling

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Computer Simulation & Modeling

Paper I

Section I


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Mahatma Gandhi Missions

College of Computer Science & Information Technology

At junction NH4 Sion-Panvel Expressway, Kamothe,Navi Mumbai-410 209.

M.Sc.(IT)PART-I

CERTIFICATE

This is to certify that Mr. kirtikumar dilip

giripunje of M.Sc.(IT)Part-I. Roll No. 17 has

completed the course of necessary practicals in

the subject of Computer Simulation & Modeling

under my supervision during the academic year

2010-2011.


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_________________

__________________Lecture-In-Charge

principal

_________________

__________________

External Examiner

External Examiner

INDEX


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Sr.

No

Date

Topic

Pag

e

No.

Sign

1. Single Sever Queuing

Model

2. Two Sever Queuing

Model

3. Newspaper Seller Problem

4. Discrete Distribution

1.Bernoulli Distribution

2.Binominal

Distribution

3.Geometric

Distribution

4.Poisson Distribution

5. Continuous Distribution

1. Uniform Distribution


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2. Exponential

Distribution

3. Gamma Distribution

4. Weibull Distribution

5. Normal Distribution

6. Triangular

Distribution

7. Erlang Distribution

6. Generate Random

Number

1. Linear Congruetial

Method

2. Multi Congruetial

Method

3. Inverse Transform

Tech.

4. Accept / Reject Tech.


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7

.

Random Number Test

1. Frequency Test

2. Run Up / Down

3. Run Above / Below

4. Autocorrelation

5. Poker Test

8. Goodness of Fit Test

Kolmogorov-Smirnov

Practical No. 1

Aim- To Implement a Single Server queuing problem

using EXCEL / C


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Code:

#include

#include

#include#include

#include

#include

void main()

{

clrscr();

int i,j;//with this statement diff random no will be generated

every time

time_t t;

srand((unsigned) time(&t));

//inter arrival variables

int arrtime[20],arrrandom[20];float arrprob[20],cdf=0,arrcdf[20];

//service time variables

int sertime[20],serrandom[20];float

serprob[]={0,0.05,0.1,0.2,0.3,0.25,0.1};//probability for

service tablefloat sercdf[20];

//simulation table variables

int rnoarr[20];

int rnoser[20];

int arrivaltime[20],clocktime[20];

int servicetime[20],servicein[20],serviceout[20];int waittime[20],idletime[20];


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float wait=0,idle=0,service=0,timespent=0;

//input arrival time table

for(i=1;i


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cout


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cout


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{

rnoarr[i]=random(1000);

}

for(i=1;i


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}

//calculating clock time

cdf=0;

for(i=1;i


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//calculating clock time

for(i=1;i


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wait=wait+waittime[i];

service=service+servicetime[i];

}

idle=idle/20;wait=wait/20;

service=service/20;

timespent=wait+service;

cout


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Practical No. 2

Aim: To Implement a two sever system using EXCEL /

C

Code:

#include

#include

#include

#include

#include

#define SIZE 15

void main()

{

//initialization

int i,j,k,a,b;int cn,atime,stime,temp,rnum;

float time], ssrand[SIZE] ], bfiveA[SIZE],

bfiveB[SIZE];

float ccn[SIZE], aatime[SIZE], sstime[SIZE],

arand[SIZE], aarand[SIZE], srand[SIZE;

float second[SIZE], third[SIZE], fourA[SIZE],fourB[SIZE], afiveA[SIZE], afiveB[SIZE;

float aprob[SIZE], acdf[SIZE], sprob[SIZE],

scdf[SIZE];

float astime, asstime[SIZE], asprob[SIZE],

ascdf[SIZE];

float bstime, bsstime[SIZE], bsprob[SIZE],

bscdf[SIZE];


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int asrand[SIZE], bsrand[SIZE];

clrscr();

coutcn;

for(i=0;i


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for(j=0;j


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//beaker service();

coutbstime;

cout


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cout


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}

cout


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aarand[a]=rnum;

a++;

}

}

if(b


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third[i]=0;

afiveA[i]=0;

bfiveA[i]=0;

}

else

{

arand[-1]=1;

//val for 2nd

for(j=0;jarand[j-1] &&

aarand[i]=afiveB[i-1])

{

if(afiveB[i-1]>third[i])

{

afiveA[i]=afiveB[i-1];

}

else


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{

afiveA[i]=third[i];

}

bfiveA[i]=0;

bfiveB[i]=0;

}

else if(third[i]>bfiveB[i-1])

{

if(bfiveB[i-1]>third[i])

{bfiveA[i]=bfiveB[i-1];

}

else

{

bfiveA[i]=third[i];

}afiveA[i]=0;

afiveB[i]=0;

}

}

srand[-1]=1;

if(afiveB[i-1]


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{

fourA[i]=asstime[k];

fourB[i]=0;

break;

}

}

}

else

{

for(k=0;kbsrand[k-1] &&

ssrand[i]=afiveB[i-1])

{

afiveB[i]=fourA[i]+afiveA[i];

bfiveB[i]=0;

}

else if(third[i]>bfiveB[i-1])


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{

bfiveB[i]=fourB[i]+bfiveA[i];

afiveB[i]=0;

}

afiveB[-1]=0;

}

cout


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"


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Practical No. 3Aim: To Implement a Newspaper seller problem.

Code:

#include

#include

#include

#include

#include

#define SIZE 15

void main()

{

int i, j, k, a, b, rnum, avgdemand, value=0;


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int day, tdemand, type, salecost, salvagecost, price,

salvageprice;

int days[SIZE], demand[SIZE], trand[SIZE],

grand[SIZE], frand[SIZE], prand[SIZE];

int ttype[SIZE], ttdemand[SIZE], revenue[SIZE],

drand[SIZE], nrand[SIZE];

float cdf[SIZE], good[SIZE], poor[SIZE], fair[SIZE];

float lost[SIZE], salvage[SIZE], profit[SIZE];

float pg, pf, pp;

clrscr();coutday;

for(i=0;i>pg;

cout>pf;

cout>pp;

//cumulative prob

for(i=0;i


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{

if(i==0)

cdf[i]=pg;

else if(i==1)

cdf[i]=cdf[i-1]+pf;

else if(i==2)

{

cdf[i]=cdf[i-1]+pp;

value=cdf[i];

}}

coutprice;

cout>salecost;

cout>salvagecost;

cout


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cout>tdemand;

cout


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grand[i]=good[i]*100;

fair[i]=fair[i]+fair[i-1];

frand[i]=fair[i]*100;

poor[i]=poor[i]+poor[i-1];

prand[i]=poor[i]*100;

}

//big table

//random num for demand & newspaper

a=0,b=0;

while(a


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cout


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}

}

}

else if(ttype[j]==2) //fair

{

for(i=1;i


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if(ttdemand[j]


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cout


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for(k=0;k


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Output:-

1. Input Values


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2. Output Values


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Practical No. 4

Aim: Simulate the following discrete distribution.

1. Program to find the probability mass function (pmf)p(X), meanE(X) and variance V(X), for theBernoulli destruction. Accept the probability of success

p, the probability of failure q, no. of trails n form the

user and display the value of pmf.

Code:

#include

#include

#include

#include

#include

void main(){

//initialization

int x,i,n;

float p,q,pdf,mean,variance;

float temp;

clrscr();


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cout>p;

if(p>0 && pn;

cout


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getch();

}


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Output:-


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2. Program to find the probability mass function (pmf)

p(X), mean

E(X) and variance

V(X), for theBinomial destruction. Accept the probability of success

p, the probability of failure q, no. of trails n form the

user and display the value of pmf.

Code:

#include#include

#include

#include

#include

void main()

{//initialization

int x,i,j,n;

float p,q,pdf,mean,variance;

float temp,r=1,s=1,t=1,c;

clrscr();


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cout>p;

if(p>0 && p


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}

//mean

mean=n*p;

variance=n*p*q;

cout


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Output:-


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p(X), meanE(X) and variance V(X), for thePoisson destruction. Accept the probability of success p,

the probability of failure q, no. of trails n form the user

and display the value of pmf.

Code:

#include

#include

#include

#include

#include

#define SIZE 15

void main()

{

float p,q,x,lam,a=1,pdf,mean,vari;

int n,i;


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clrscr();

coutp;

if (p>0 && p


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{

cout


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Output:-


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p(X), mean

E(X) and variance

V(X), for theGeometric destruction. Accept the probability of

success p, the probability of failure q, no. of trails n

form the user and display the value of pmf.

Code:

#include


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#include

#include

#include

#include

void main()

{

float p,q,x,pdf,mean,vari;

int n,i;

clrscr();

coutp;

if (p>0 && p


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cout


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Output:-


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Practical No. 5

Aim: Simulate the following continuous distribution

1. Program to find probability distribution function

(PDF) and cumulative distribution function (CDF) for

Uniform distribution accept parameters a and b from

the user for the random variable X which is distributed

uniformly between a and b.


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Code:

#include

#include

#include

#include

#include

void main()

{

float pdf,cdf,a,b;

int n,i,x;

clrscr();

cout>a;

cout>b;

pdf=(1/(b-a));

cout


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Output:-


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Exponential distribution accept parameters a and b

from the user for the random variable X which is

distributed uniformly between a and b.

Code :

#include#include

#include

#include

#include

void main()

{

float cdf,a,b,lam;

int i,x;

double pdf;

clrscr();

cout>lam;

cout


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cin>>x;

cout


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Exponential distribution accept parameters a and b

from the user for the random variable X which is

distributed uniformly between a and b.


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Code :

#include

#include

#include

int facto(int be)

{

int i,prod=1;

for(i=be;i>=1;i--)

{

prod=prod*i;

}

return prod;

}

void main(){

float b,t,pdf,cdf,var,mean,sum=0.0;

clrscr();

coutb;coutt;

mean=(float)(1/t);

var=(float)(1/(b*t));

int b1=b-1;

cout


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cout


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Output:-


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Weibull distribution.

Code :

#include


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#include

#include

int facto(int x)

{

int i,prod=1;

x=x-1;

for(i=x;i>=1;i--)

{

prod=prod*i;}

return prod;

}

void main()

{

float b,a,v,temp,temp1,x;float pdf,cdf,var,mean;

clrscr();

coutb;

couta;

coutv;

float b1,b2,b3,b4;

b1=(1/b)+1;

b2=facto(b1);

mean=v+(a*b2);

b3=facto((2/b)+1);


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b4=b3-(pow(b2,2));

var=a*a*b4;

cout


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cdf=1-exp(temp);

}

//end of cdf

cout


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Output:-


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Normal distribution.

Code :

#include

#include

#include#include

#define SIZE 20

void main()

{

int i;

int rove,mue,range,x[SIZE];float a,b,c,d,pdf[SIZE];

clrscr();

cout>rove;

cout>mue;

coutrange;

cout


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cout


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Output:-


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Triangular distribution.

Code :

#include

#include

#include

#include

#define SIZE 20

void main()

{

int i;

int alpha,beta,range,v;

float a,b,c,d,pdf[SIZE];

float x[SIZE];

clrscr();

cout


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cout>beta;

cout>v;

coutrange;

cout


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}


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Output:-


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Practical No.6

Aim: To generate random numbers and random

variates

1. To generate random numbers using linear

congruential method

Code:

#include

#include

#include

#include

#define SIZE 20

void main()


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{

//initialization

int i;

int num,a,c,x0,m,x[SIZE];

float r[SIZE],xr[SIZE];

clrscr();

coutx0;

cout>a;

cout>c;

cout>m;

x[0]=x0;

for(i=1;i


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r[i]=xr[i]/m;

}

//print

cout


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Output:-


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2. To generate random numbers using multiplicative

congruential method

Code:

#include

#include

#include


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xr[i]=x[i];

r[i]=xr[i]/m;

}

//print

cout


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Output:-


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3. To generate random variates using Inverse

Transform Tecchnique

a. Exponential Distribution :

F(x) = 1-e x/

Where x>=0 and find F-1 (u) = - In (1-u)

Code :

#include#include

#include

#include

#include

#include

void main()

{

clrscr();

time_t t;


int n,i;

float a,b,x[100],r[100],lambda;cout


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cout


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B. Uniform Distribution

F(x) = x-a / b-a = R x = a + (b-a) R

Code:

#include


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#include

#include

#include

#include

void main()

{

clrscr();

time_t t;


int n,i;

float a,b,x[100],r[100];

cout


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}

Output:-


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4. TO generate random variates using Acceptance-

Rejection Technique

Code:

#include

#include

#include

#include

#include#include

#include

void main()

{

clrscr();

time_t t;


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int i=1,x,n=100;

float p,r,lambda,e;

cout


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x++;

p=p*r;

cout


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Output:-


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Practical No. 7

Testing of Random Number

1. Aim: To test the uniformity of the random numbers

using frequency test.

Code:

#include

#include


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#include

#include

void main()

{

clrscr();

int i,n,j,e=10,x[101],o[11];

float

r[101],chical,chitable,z,y,range[]={0.0,0.1,0.2,0.3,0.4,0.5,0.

6,0.7,0.8,0.9,1.0};

double c,alpha;cout


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cout


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if(r[i] < c)

{

o[j]=o[j]+1;

break;

}

else

c=c+0.1;

}}

cout


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}

cout


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Output:-


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2. Aim: To test the uniformity of the random no. using

Runs Ups & Runs Down as well as Runs Above & Below

Mean

i. Runs Ups & Runs Down have the mean & variance as

a = 2N -1 / 3 , 2a = 16N -29 / 90

Z0 = 1 -a / a


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Code:

#include#include

#include

#include

#include

#include

void main()

{

clrscr();

float r[21],meu,sigma,s,zcal,ztable;

int n,i,count=0,sign[21];

time_t t;


cout>n;

cout


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}

for(i=1;i


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else

sign[i]=0;

}sign[20]=1;

//calculating no. of runs

for(i=2;i


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cout


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Output:-


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Code:

#include

#include

#include

#include

#include

#include

void main()

{

clrscr();

float r[21],meu,sigma,s,zcal,ztable,sum=0,x;

int n=20,i,count=0,sign[21],n1=0,n2=0,alpha;

float a,b,c,d;

time_t t;


//generating random nos.

for(i=1;i


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cout


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else

{

sign[i]=1;

n2++;

}

}

//calculating no. of runs

for(i=2;i


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cout


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getch();

}

Output:-


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4. Aim: To test the uniformity of the random no. using

Autocorrelation

Code:


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#include

#include

#include

#include

#include

#include

void main()

{

clrscr();

time_t t;


float r[51],ztable,sum=0,d=0,e=0,row=0,sigma,zcal;

int i,n,j,lag,M=0,alpha,a=0,b=0,c=0;

cout


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cout


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//calculating row,sigma,zcal

for(j=0;j


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cout


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Output:-


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5. Aim: To test uniformity of the random no. using

Pokers test

Code:

#include

#include

#include

#include


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#include

#include

void main()

{

clrscr();

time_t t;


float r[51],ztable,sum=0,d=0,e=0,row=0,sigma,zcal;int i,n,j,lag,M=0,alpha,a=0,b=0,c=0;

cout


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cout


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{

b=i+j*lag;

c=i+(j+1)*lag;

d=r[b]*r[c];

sum=sum+d;

}

e=(float)1/(M+1);

row=(e*sum)-0.25;

d=0;d=13*M+1;

d=sqrt(d);

sigma=d/(12*(M+1));

zcal=row/sigma;

zcal=fabs(zcal);

//displaying the values

cout


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cout


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Output:-


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Practical No.8

Aim: To perform goodness of fit test using Kolmogorov

- Smirnov

Code:


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#include

#include

#include

#include

#include

void main()

{

clrscr();

int i,j,k=1,alpha,num=10;double D1[50],D2[50];

double Dcal,s;

double dtable,temp;

double cdf=0,arrival[50],normalize[50];

double r[50];

//generating interarrival times through random

function

for(i=0;i


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if(alpha==1)

dtable=0.490;

else if(alpha==5)

dtable=0.410;

else

dtable=0.368;

cout


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{

normalize[i]=arrival[i]/100;

}

for(i=0;i


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temp=0.0;

for(i=0;i


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cout


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}

else

{

cout


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