1. Brief description
Calculation of probability distribution laws and density function values
Matlab directly provides a general function to calculate the value of the probability density function. They are pdf and namepdf functions, which are used as follows:
Y=pdf('name', K, A, B) or: namepdf (K, A, B)
above The function means to return the probability value or density value at X=K and the parameters are A, B, and C. For different distributions, the number of parameters is different; name is the name of the distribution function, which needs to be changed according to the corresponding distribution when used. The function names are summarized in the following table:
Value of name Function Description
'beta' or 'Beta' Beta distribution
'bino' or 'Binomial' Binomial distribution
'chi2' or 'Chisquare' Chi-square distribution
'exp' or 'Exponential' Exponential distribution
'f' or 'F ' F distribution
'gam' or 'Gamma' GAMMA distribution
'geo' or 'Geometric' geometric distribution
'hyge' or 'Hypergeometric' hypergeometric distribution
'logn' or 'Lognormal' lognormal distribution
'nbin' or 'Negative Binomial' ' Negative binomial distribution
'ncf' or 'Noncentral F' Noncentral F distribution
'nct' or 'Noncentral t' Noncentral t distribution
'ncx2' or 'Noncentral Chi-square' Noncentral chi-square distribution
'norm' or' Normal' Normal distribution
'poiss' or 'Poisson' Poisson distribution
'rayl' or 'Rayleigh' Rayleigh distribution
't' or 'T' T distribution
'unif' or 'Uniform' Continuous uniform distribution
'unid' or 'Discrete' Uniform' discrete uniform distribution
'weib' or 'Weibull' Weibull distribution
2. Code and running results
%% Density function of binomial distribution
clear all;
x=1:20;
y=binopdf(x,200,0.06);
figure;
plot(x,y,'r*');
title('Binomial distribution (n =200, p=0.06)');
%% Poisson distribution density function
clear all;
x=1:20;
y=poisspdf(x,20); %Poisson distribution
figure;
plot(x,y,'r+');
title('Poisson distribution' );
%% geometric distribution
clear all;
x=1:10;
y=geopdf(x,0.4); % geometric distribution
figure;
plot(x,y,'rx');
title('geometric distribution');
%% Uniform distribution (discrete)
clear all;
n=10;
x=1:n;
y=unidpdf(x,n); % Uniform distribution (discrete)
figure;
plot(x,y,'ro');
title( 'Uniform distribution (discrete)');
%% Uniform distribution (continuous)
clear all;
x=-2:0.1:15;
y=unifpdf(x,0,6); % Uniform distribution (continuous) between 0 and 6
figure;
plot(x,y,' r:');
title('Uniform distribution (continuous)');
%% Exponential distribution
clear all;
x=0:0.1:10;
y=exppdf(x,2); % Exponential distribution
figure;
plot(x,y,'r:');
title('Exponential distribution');
%% normal distribution
clear all;
x=-5:0.1:5;
y1=normpdf(x,0,1); % standard normal distribution
y2=normpdf(x,3,3); % non-standard normal distribution
figure;
plot(x,y1,x,y2,':');
legend('standard normal distribution','non-standard normal distribution');
x1=-5:0.1:5;
y3=normpdf(x1, 3,1); %SIGMA=1
y4=normpdf(x1,3,2); %SIGMA=2
y5=normpdf(x1,3,3); %SIGMA=3
figure
plot(x1,y3,'r-',x1,y4,'b:',x1,y5,'k--');
legend('SIGMA=1','SIGMA=2','SIGMA=3');
y6=normpdf(x1,0,2); %MU=0
y7=normpdf(x1,2,2); %MU=2
y8=normpdf(x1,4,2); %MU=4
figure
plot(x1,y6,'r-',x1,y7,'b:',x1,y8,'k--');
legend('MU=0','MU=2','MU=4');
%% The probability density function of the three major sampling distributions
%% Chi-square distribution
clear all;
x=0:0.1:15;
y1=chi2pdf(x,2); %Chi-square distribution n=2
y2=chi2pdf(x,3) ; % chi-square distribution n=3
figure;
hold on;
plot(x,y1);
plot(x,y2,':');
legend('n=2','n=3');
title('card square distribution');
%% t distribution
clear all;
x=-5:0.1:5;
y1=tpdf(x,2); %t distribution (n=2)
y2=tpdf(x,10); %t distribution (n=10)
figure;
plot(x,y1,'r:',x,y2,'b-');
legend('n=2','n=10');
title('t distribution');
%% F distribution
clear all;
x=0.1:0.1:5;
y=fpdf(x,2,5); %F distribution
figure;
plot(x,y,'r:');
title('F distribution (m =2,n=5)');
