Normal Distribution - using 24x45x65 matrix. - How to do this?

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awda 2014-4-22

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评论： Star Strider 2014-4-24

x_weekday.mat

Hello

I have a set of data in a matrix of: 24x45x65 --> hours x days x customers i want to make a normal distribution plot for each hour of lets say 1 customer on y-axis. so there will be 24 Graphs. then i can show the mean of it..lower and upper boundry on the plot. its data of some customers using energy in different times of the day..(before going to Work and coming back from the Work) example(used pain

t :P)

is it possible to do so? i will include my data to this file..so its easier to understand :)

thanks in advance, help will be appreciated alot.

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Answer 1

Star Strider 2014-4-22

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https://ww2.mathworks.cn/matlabcentral/answers/126678-normal-distribution-using-24x45x65-matrix-how-to-do-this#answer_134171

编辑：Star Strider 2014-4-22

在 MATLAB Online 中打开

This seems to work:

load x_weekday
xwkd = x_weekday;
for k1 = 1:size(xwkd,1)
    hrmx = xwkd(k1,:,:);            % All data for hour ‘k1’
    hrmn(k1) = mean(hrmx(:));       % Mean
    hrsd(k1) = std(hrmx(:));        % Standard deviation
end
N = numel(hrmx);
figure(2)                           % Plot Mean ± Standard Deviation
errorbar([1:24], hrmn, hrsd)
grid
xlabel('Hour')
ylabel('kWh ± SD') 
figure(3)                           % Plot Mean ± Standard Error
errorbar([1:24], hrmn, hrsd/sqrt(N))
grid
xlabel('Hour')
ylabel('kWh ± SE')

It plots the data for all customers. To plot data for a particular customer, say Customer #10, change this line:

hrmx = xwkd(k1,:,:); % All data for hour ‘k1’

to:

hrmx = xwkd(k1,:,10); % All data for Customer 10 for hour ‘k1’

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Star Strider 2014-4-22

编辑：Star Strider 2014-4-23

在 MATLAB Online 中打开

Would a 3D surface plot of the normally-distributed data with interpolation do what you want? I’ll work on that, since the same code can also be used for other plots like contour.

Figure 1 plots usage and ±1 standard deviation error bars. Figure 2 plots usage and standard error error bars, actually more statistically meaningful and useful. Since the means have an inherent error most accurately described by the standard error (that is normally distributed) rather than the standard deviation, I will plot the standard errors and their distributions.

A FEW HOURS LATER ...

load x_weekday
xwkd = x_weekday;
for k1 = 1:size(xwkd,1)
    hrmx = xwkd(k1,:,:);            % All data for hour ‘k1’
    hrmn(k1) = mean(hrmx(:));       % Mean
    hrsd(k1) = std(hrmx(:));        % Standard deviation
end
n = numel(hrmx);
hrse = hrsd/sqrt(n);
Npdf = @(x,mu,s) exp(-(0.5.*(x-mu)/s).^2) / (s*sqrt(2*pi));
x = 1:size(xwkd,1);
y = linspace(0,5);
[X,Y] = meshgrid(x,y);
z = zeros(length(y),length(x));
for k1 = 1:length(x)
    Z(:,k1) = Npdf(y, hrmn(k1), hrsd(k1));
end
figure(4)
surfc(X, Y, Z)
xlabel('Hour')
ylabel('kWh')
zlabel(' Probability')
view(-160, 60)
grid on

You can rotate the plot you generate interactively to view it from different angles. You can also substitute contour for surfc if you want a contour plot. If you want to see more of the kWh axis, change the upper limit in this statement from 5 to something else:

y = linspace(0,5);

Star Strider 2014-4-23

编辑：Star Strider 2014-4-23

Yes!

They are Gaussian curves, but (correctly) using the standard error of the mean rather than the standard deviation. The Normal distribution curve is symmetrical, but deliberately cuts off at zero kWh, since unless your customers have solar panels or windchargers and are feeding power back into the electrical power grid, all usage will be greater than zero. [There are probability distributions that will always be greater than zero (the lognormal being one), but the distribution has to be used in context, and unless you know that the data are best described by another distribution, using the normal distribution for the standard error is dictated by the Central Limit Theorem. The CLT probably applies anyway, since the number of observations, 2925 in each Hour, is likely sufficient.]

The colors are a convenient way of depicting the relative magnitude of the function at various locations in the plot. You can redefine them to be a different colorbar if you want to.

I do not understand ‘what about the probability 1 to 4’. If you mean Hours 1 to 4, I suspect that everyone is at home asleep and power usage is minimal and relatively consistent among the Customers and Days, so the standard errors are lowest then. (The same pattern evolves between Hours 20 through 24.) That is simply a guess on my part, but seems logical.

Not ‘bad’ at all! I will do my best to explain what I do in my code, and why, to the the best of my knowledge and ability.