Creating a histogram by super imposing a normal distribution h = histogram(data,’Normalization’,’probability’)

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Creating a histogram by super imposing a normal distribution h = histogram(data,’Normalization’,’probability’);

The correct answer and explanation is :

To create a histogram of your data and superimpose a normal distribution curve in MATLAB, you can use the histfit function, which simplifies this process. Here’s how you can do it:

% Generate sample data (e.g., 1000 random numbers from a normal distribution)
data = randn(1000,1);

% Create a histogram with a superimposed normal distribution fit
histfit(data);

This code will produce a histogram of your data with a normal distribution curve fitted and overlaid on the histogram.

Explanation:

  1. Generating Sample Data:
    In this example, we use randn(1000,1) to generate 1000 random numbers from a standard normal distribution (mean = 0, standard deviation = 1). Replace this with your actual dataset.
  2. Creating the Histogram with histfit:
  • The histfit function in MATLAB creates a histogram of the data and fits a normal density function to it. By default, it fits a normal distribution, but you can specify other distributions if needed.
  • The function automatically calculates the mean and standard deviation of your data and plots the corresponding normal distribution curve over the histogram.

Understanding the Output:

  • Histogram Bars:
    The histogram represents the frequency distribution of your data, showing how often data points fall within specific ranges (bins).
  • Normal Distribution Curve:
    The superimposed curve represents the probability density function (PDF) of a normal distribution with the same mean and standard deviation as your data. This visual comparison helps assess how closely your data follows a normal distribution.

Customization:

  • Number of Bins:
    By default, histfit determines the number of bins based on the data size. To specify the number of bins, use:
  histfit(data, numberOfBins);

Replace numberOfBins with your desired number.

  • Normalization:
    To normalize the histogram so that the area under the bars sums to 1 (making it a probability density function), you can use the ‘Normalization’ property:
  histogram(data, 'Normalization', 'pdf');
  hold on;
  x = linspace(min(data), max(data), 100);
  y = normpdf(x, mean(data), std(data));
  plot(x, y, 'r-', 'LineWidth', 2);
  hold off;

Here, histogram creates a normalized histogram, and normpdf computes the normal distribution values, which are then plotted over the histogram.

Considerations:

  • Data Normality:
    Visual inspection using this method provides an initial assessment of normality. For a more rigorous evaluation, consider using statistical tests such as the Kolmogorov-Smirnov test or the Shapiro-Wilk test.
  • Sample Size:
    With small sample sizes, the histogram may not accurately represent the underlying distribution, making it harder to assess normality. In such cases, normal probability plots (Q-Q plots) can be more informative.

Conclusion:

Superimposing a normal distribution curve over a histogram in MATLAB using histfit is a straightforward and effective way to visually assess how well your data conforms to a normal distribution. This method provides immediate visual feedback, aiding in the preliminary analysis of your dataset’s distribution characteristics.

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