lower and upper cusum

Hello,

I'm trying to use the cusum to evaluate the upper and lower cumulative sums as;

y=random('normal', 7.0,0.1,10,1);      [iu il Cp Cm]=cusum(y);

However, the evaluated Cp and Cm do not match the figure when use

cusum(y);

Answer 1

[Adam Danz]

Notice the ylabel in the plot generated by cusum. It's standard error. To convert the upper and lower sums to standard error, divide the Cp and Cm by the target standard deviation value shown in the title of the axes.

Note that if you don't provide cusum with the target mean and target standard deviation, those values are computed internally based on up to the first 25 samples of your data (see doc page).

Here's how to compute those lines given your inputs.

y=random('normal', 7.0,0.1,10,1);      

% produce plot
cusum(y)

% Compute std-error based on first 25 samples
[iu il Cp Cm]=cusum(y);
ySamples = y(1:min(25,numel(y)));
t = max(eps(class(y)),std(ySamples));
CpStdErr = Cp/t; 
CmStdErr = Cm/t; 

% Plot dashed lines showing the computed values. 
hold on 
plot(1:numel(CpStdErr),CpStdErr, 'b--','LineWidth',2)
plot(1:numel(CmStdErr),CmStdErr, 'r--','LineWidth',2)

[Amr Sadek]

Thanks Adam, it works.

Answer 2

[Sulaymon Eshkabilov]

Note that every time, when you run the command it generates a new set of values. Thus, use rng():

rng('default')
y=random('normal', 7.0,0.1,10,1);      
[iu il Cp Cm]=cusum(y)

iu =

  0×1 empty double column vector


il =

  0×1 empty double column vector

Cp = 10×1

0 0.0325 0 0 0 0 0 0 0.2069 0.3329

Cm = 10×1

0 0 -0.1998 -0.0875 -0.0296 -0.1343 -0.1516 -0.0913 0 0

% OR specify the seed value, e.g., 13
rng(13)  
y=random('normal', 7.0,0.1,10,1);      
[iu il Cp Cm]=cusum(y)

iu =

  0×1 empty double column vector


il =

  0×1 empty double column vector

Cp = 10×1

0 0 0.0504 0.0290 0.1130 0 0 0.0080 0 0

Cm = 10×1

0 -0.1428 -0.0016 0 0 -0.0383 -0.0199 0 0 0

% Test the seed value, e.g., 13
rng(13)  
y=random('normal', 7.0,0.1,10,1);      
[iu il Cp Cm]=cusum(y)

iu =

  0×1 empty double column vector


il =

  0×1 empty double column vector

Cp = 10×1

0 0 0.0504 0.0290 0.1130 0 0 0.0080 0 0

Cm = 10×1

0 -0.1428 -0.0016 0 0 -0.0383 -0.0199 0 0 0