I guess this is an easy question, but I have been struggling to solve it. Is it possible to create a Normal Distribution in Matlab purely based on the mean and Standard Deviation? I don't know what the x values are and therefore unable to use the normpdf() function.
Thanks
The randn function can do that for you.
The documentation give this example :
Generate values from a normal distribution with mean 1 and standard
deviation 2:
r = 1 + 2.*randn(100,1);
Related
I am trying to obtain an equation for a function fitted to some histogram data, I was thinking of trying to do this by fitting a rational function as the data doesn't resemble any distribution recognisable by myself.
The data is experimental, and I want to be able to generate a random number according to its distribution. Hence I am hoping to be able to fit it to some sort of PDF from which I can obtain a CDF, which can be rearranged to a function into which a uniformly distributed random number between 0 and 1 can be substituted in order to obtain the desired result.
I have attempted to use the histfit function, which has worked but I couldn't figure out how to obtain an equation for the curve it fitted. Is there something stupid I have missed?
Update: I have discovered the function rationalfit, however I am struggling to figure out what the inputs need to be.
Further Update: Upon exploring the histfit command further I have discovered the option to fit it to a kernal, the figure for which looks promising, however I am only able to obtain a set of x and y values for the curve, not its equation as a I wanted.
From the documentation on histfit:
Algorithms
histfit uses fitdist to fit a distribution to data. Use fitdist
to obtain parameters used in fitting.
So the answer to your question is to use fitdist to get the parameters you're after. Here's the example from the documentation:
rng default; % For reproducibility
r = normrnd(10,1,100,1);
histfit(r)
pd = fitdist(r,'Normal')
pd =
NormalDistribution
Normal distribution
mu = 10.1231 [9.89244, 10.3537]
sigma = 1.1624 [1.02059, 1.35033]
y = gauss(x,s,m)
Y = normpdf(X,mu,sigma)
R = normrnd(mu,sigma)
What are the basic differences between these three functions?
Y = normpdf(X,mu,sigma) is the probability density function for a normal distribution with mean mu and stdev sigma. Use this if you want to know the relative likelihood at a point X.
R = normrnd(mu,sigma) takes random samples from the same distribution as above. So use this function if you want to simulate something based on the normal distribution.
y = gauss(x,s,m) at first glance looks like the exact same function as normpdf(). But there is a slight difference: Its calculation is
Y = EXP(-(X-M).^2./S.^2)./(sqrt(2*pi).*S)
while normpdf() uses
Y = EXP(-(X-M).^2./(2*S.^2))./(sqrt(2*pi).*S)
This means that the integral of gauss() from -inf to inf is 1/sqrt(2). Therefore it isn't a legit PDF and I have no clue where one could use something like this.
For completeness we also have to mention p = normcdf(x,mu,sigma). This is the normal cumulative distribution function. It gives the probability that a value is between -inf and x.
A few more insights to add to Leander good answer:
When comparing between functions it is good to look at their source or toolbox. gauss is not a function written by Mathworks, so it may be redundant to a function that comes with Matlab.
Also, both normpdf and normrnd are part of the Statistics and Machine Learning Toolbox so users without it cannot use them. However, generating random numbers from a normal distribution is quite a common task, so it should be accessible for users that have only the core Matlab. Hence, there is a redundant function to normrnd which is randn that is part of the core Matlab.
I am trying to perform a multiple linear regression in MATLAB using the regress function, and I am using a number of different variables that involve different scales and units. I am assume the answer to this question is yes, but should I normalize each variable before running the regression? I'm not sure if MATLAB does so automatically. Thanks for the help!
Yes, you should. If you want to normalize it between 0 and 1, you could use mat2gray function (assuming "vector" as your list of variables).
norm_vect = mat2gray(vector);
This function is used to convert matrix into an image, but works well if you don't want to write yours. You also can use a simple normalization like:
for i = 1:length(vector)
norm_vect(i) = (vector(i)-min(vector))/(max(vector)-min(vector));
end
I am wondering how, in Matlab, to plot a continuous pdf with the following information?
mean=-0.3731
standard deviation= 5.6190
skewness=-3.0003
kurtosis=13.1722
or alternative how do I plot a continous pdf that is not normal? (like it is skewness and has kurtosis, etc)
Thanks!
Those parameters don't define a distribution, but normally you would use "makedist" in matlab to generate a probability distribution object and then plot it.
The following thread has some discussion on defining a distribution. How to generate distributions given, mean, SD, skew and kurtosis in R?
Based on your comment below, I think you are looking for something like the following functio that generates a m by n matrix of random values with the following parameters:
r = pearsrnd(mu,sigma,skew,kurt,m,n)
I'm trying to write a generic function for finding the cosine of a value inputted into the function. The formula for cosine that I'm using is:
n
cosx = sum((-1)^n*x^(2n)/(2n)!)
n=1
I've looked at the matlab documentation and this page implies that the "sum" function should be able to do it so I tried to test it by entering:
sum(x^n, n=1..3)
but it just gives me "Error: The expression to the left of the equals sign is not a valid target for an assignment".
Is summing an infinite series something that matlab is able to do by default or do I have to simulate it using a function and loops?
Well if you want to approximate it to a finite number of terms you can do it in Matlab without toolboxes or loops:
sumCos = #(x, n)(sum(((-1).^(0:n)).*(x.^(2*(0:n)))./(factorial(2*(0:n)))));
and then use it like this
sumCos(pi, 30)
The first parameter is the angle, the second is the number of terms you want to take the series to (i.e. effects the precision). This is a numerical solution which I think is really what you're after.
btw I took the liberty of correcting your initial sum, surely n must start from 0 if you are trying to approximate cos
If you want to understand my formula (which surely you do) then you need to read up on some essential Matlab basics namely the colon operator and then the concept of using . to perform element-wise operations.
In MATLAB itself, no, you cannot solve an infinite sum. You would have to estimate it as you suggested. The page you were looking at is part of the Symbolic Math toolbox, which is an add-on to MATLAB. In particular, you were looking at MuPAD, which is rather similar to Mathematica. It is a symbolic math workspace, whereas MATLAB is more of a numeric math workspace. If you own the Symbolic Math toolbox, you can either use MuPAD as you tried to above, or you can use the symsum function from within MATLAB itself to carry out sums of series.