Plot Pdf Matlab From Data

Key focus: Shown with examples: let’s estimate and plot the probability density function of a random variable using Python’s Matplotlib histogram function.

Plotting Data Using MATLAB: In this tutorial you will learn how to use the MATLAB program from MathWorks to create a script file that will make a set of data and plot that data. This is a very useful tool in all types of scientific and math based research allowing the user to. This MATLAB function returns the probability density function (pdf) for the one-parameter distribution family specified by 'name' and the distribution parameter A, evaluated at the values in x. For example, plot(X,Y,'y-',X,Y,'go') plots the data twice, with a solid yellow line interpolating green circles at the data points. The plot command, if no color is specified, makes automatic use of the colors specified by the axes ColorOrder property.

Note: If you are inclined toward programming in Matlab, visit here.

Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s see how we can generate a simple random variable, estimate and plot the probability density function (PDF) from the generated data and then match it with the intended theoretical PDF. Normal random variable is considered here for illustration.

Step 1: Generate random samples

Plot Pdf Matlab From Data Set

A survey of commonly used fundamental methods to generate a given random variable is given in [1]. For this demonstration, we will consider the normal random variable with the following parameters : – mean and – standard deviation. First generate a vector of randomly distributed random numbers of sufficient length (say 100000) with some valid values for and . There are more than one way to generate this. Two of them are given below.

● Method 1: Using the in-built numpy.random.normal() function (requires numpy package to be installed)

Matlab Plot Pdf From Data

● Method 2: Box-Muller transformation [2] method produces a pair of normally distributed random numbers () by transforming a pair of uniformly distributed independent random samples (). The algorithm for transformation is given by

Step 2: Plot the estimated histogram

Typically, if we have a vector of random numbers that is drawn from a distribution, we can estimate the PDF using the histogram tool. Matplotlib’s hist function can be used to compute and plot histograms. If the density argument is set to ‘True’, the hist function computes the normalized histogram such that the area under the histogram will sum to 1. Estimate and plot the normalized histogram using the hist function.

Plot Pdf Matlab From Data Sheet

Step 3: Theoretical PDF:

And for verification, overlay the theoretical PDF for the intended distribution. The theoretical PDF of normally distributed random samples is given by

Theoretical PDF for normal distribution is readily obtained fromstats.norm.pdf() function in the SciPy package.

The histogram and theoretical PDF of random samples generated using Box-Muller transformation, can be plotted in a similar manner.

Plot Pdf Matlab From Data List

References:

[1] John Mount, ‘Six Fundamental Methods to Generate a Random Variable’, January 20, 2012
[2] Thomas, D. B., Luk. W., Leong, P. H. W., and Villasenor, J. D. 2007. Gaussian random number generators. ACM Comput. Surv. 39, 4, Article 11 (October 2007), 38 pages DOI = 10.1145/1287620.1287622 http://doi.acm.org/10.1145/1287620.1287622

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