%stat351_introduction3.m
%order statistics

>>X= exprnd(1,10,1)
X =

    0.4995
    0.7216
    0.1151
    0.2717
    0.7842
    3.9898
    0.1967
    0.8103
    0.4854
    0.2333

>>max(X)
ans =

    3.9898

>>min(X)
ans =

    0.1151

>>median(X)
ans =

    0.4925

>>Y=sort(X)
% Y is the order statistics of X.
Y =

    0.1151
    0.1967
    0.2333
    0.2717
    0.4854
    0.4995
    0.7216
    0.7842
    0.8103
    3.9898

>>Y(2)    
ans =

    0.1967
    
>>Z = expcdf(Y,1)
Z =

    0.1087
    0.1786
    0.2081
    0.2379
    0.3846
    0.3932
    0.5140
    0.5435
    0.5553
    0.9815

% probability integral transform    
X=exprnd(1,10000,1);
>> help hist

 HIST  Histogram.
    N = HIST(Y) bins the elements of Y into 10 equally spaced containers
    and returns the number of elements in each container.  If Y is a
    matrix, HIST works down the columns.
    N = HIST(Y,M), where M is a scalar, uses M bins.
hist(X,100)

Z = expcdf(X,1);
hist(Z,100)

% random number generator
Y= unifrnd(0,1,10000,1);
X= -log(1-Y);
hist(X,100)