How to generate mixture of exponential and beta distribution

Hello

I have to generate random variable from exponential and beta distribution where a=4 b=7 for beta and lamda=0.5 while p=0.8 How can i generate mixture of both?

Answer 1

[Jeff Miller]

Check whether I have interpreted your parameters correctly, but it should look something like this:

lambda = 0.5;
a = 4;
b = 7;
pr_exponen = 0.8;
n = 1000;
e = exprnd(1/lambda,n,1);
b = betarnd(a,b,n,1);
u = rand(n,1);
mix = zeros(n,1);
use_e = u < pr_exponen;
mix(use_e) = e(use_e);
mix(~use_e) = b(~use_e);
figure; histogram(mix);

[Lakshit Chugh]

Why you have use u=rand(n,1) cant we directly use like e<=0.8 ?

[Jeff Miller]

You could use e<=0.8 but that would be a different distribution, and one that is not a mixture in the usual meaning of that term. A standard mixture would sometimes include e>0.8, which would not happen if you used e<=0.8

[Lakshit Chugh]

Ok can you help me i am using the dataset but i am getting mse not valid in the same dataset i am looking to find mse of histogram estimation ?

h = 3.5*s*(length(x)).^(-1/3);

% compute the skew factor (for histograms): 
sf = ((2^(1/3))*s) / ( exp(5*s^2/4) * ((s^2 + 2)^(1/3)) * (exp(s^2) - 1)^(1/2) );
h  = h*sf; 

% get the limits, bins, bin centers etc:
x_lim_left = min(x)-1;
x_lim_rght = max(x)+1;
t0   = x_lim_left;
tm   = x_lim_rght; 
rng  = tm-t0; 
nbin = ceil(rng/h); 
bins = t0:h:(nbin*h+t0);        % <- the bin edges ... 
bc   = bins(1:end-1)+0.5*h;     % <- the bin centers ... 

x(find(x<x_lim_left))=x_lim_left;
x(find(x>x_lim_rght))=x_lim_rght;
vk=histc(x,bins); vk(end)=[];
% normalize: 
fhat = vk/(n*h);
N_MC = 10; 

xinterp = linspace( t0, tm, 15 ); 
all_mse = zeros(3,length(xinterp),N_MC);
amse    = zeros(3,1); 
for mci=1:N_MC
  %x  = exprnd(mu,1,n); % get new data 
  %x = lognrnd(1,1/2,1,n); 
  
  %  = std(x); 
  
  % the histogram estimate: 
  [bc,fhat,bins]   = norm_ref_rule_w_skew_hist(x);
  pdf_approx       = interp1(bc,fhat,xinterp,'nearest');
  
 %pdf_approx(pdf_approx>1) = 0.0; 
  sefx             = (pdf_approx - exppdf(xinterp,mu)).^2; 
  all_mse(1,:,mci) = sefx; 
  amse(1)          = amse(1) + (1/N_MC)*trapz(xinterp,sefx);
  

[Jeff Miller]

Sorry, I cannot tell what you are trying to do.