histplot plot a histogram

## Syntax

                histplot(n, data [,normalization] [,polygon], <opt_args>)
                histplot(x, data [,normalization] [,polygon], <opt_args>)
                cf = histplot(..)

## Arguments

n

  positive integer (number of classes)

x

  increasing vector defining the classes (`x` may have at least 2 components)

data

  vector (data to be analysed)

normalization

  a boolean (%t (default value) or %f)

polygon

  a boolean (%t or %f (default value))

<opt_args>

  This represents a sequence of statements `key1=value1,key2=value2` ,... where `key1`, `key2,...` can be any optional plot2d parameter (`style,strf,leg, rect,nax, logflag,frameflag, axesflag` ).

cf

  Computed frequencies (bins heighs)

## Description

This function plots a histogram of the `data` vector using the classes `x`. When the number `n` of classes is provided instead of `x`, the classes are chosen equally spaced and x(1) = min(data) < x(2) = x(1) + dx < ... < x(n+1) = max(data) with dx = (x(n+1)-x(1))/n.

The classes are defined by C1 = [x(1), x(2)] and Ci = ( x(i), x(i+1)] for i >= 2. Noting Nmax the total number of `data` (Nmax = length(data)) and Ni the number of `data` components falling in Ci, the value of the histogram for x in Ci is equal to Ni/(Nmax (x(i+1)-x(i))) when `normalization` is true (default case) and else, simply equal to Ni. When normalization occurs the histogram verifies:

\int_{x(1)}^{x(n+1)}h(x)\,\mathrm{d}x=1

when x(1)<=min(data) and max(data) <= x(n+1)

Any plot2d (optional) parameter may be provided; for instance to plot a histogram with the color number 2 (blue if std colormap is used) and to restrict the plot inside the rectangle [-3,3]x[0,0.5], you may use `histplot(n,data, style=2, rect=[-3,0,3,0.5])`.

Frequency polygon is a line graph drawn by joining all the midpoints of the top of the bins of a histogram. Therefore we can use `histplot` function to plot a polygon frequency chart.

The optional argument `polygon` connects the midpoint of the top of each bar of a histogram with straight lines.

If `polygon=%t` we will have a histogram with frequency polygon chart.

Enter the command `histplot()` to see a demo.

## Examples

Example #1: variations around a histogram of a gaussian random sample

    d = rand(1,10000,'normal');  // the gaussian random sample

    clf(); histplot(20,d);
    clf(); histplot(20,d,normalization=%f);
    clf(); histplot(20,d,leg='rand(1,10000,''normal'')',style=5);
    clf(); histplot(20,d,leg='rand(1,10000,''normal'')',style=16, rect=[-3,0,3,0.5]);

d=rand(1,10000,'normal'); clf();histplot(20,d,leg='rand(1,10000,''normal'')',style=16, rect=[-3,0,3,0.5]);

Example #2: histogram of a binomial (B(6,0.5)) random sample

    d = grand(1000,1,"bin", 6, 0.5);
    c = linspace(-0.5,6.5,8);

    clf()
    subplot(2,1,1)
    histplot(c, d, style=2);
    xtitle("Normalized histogram")

    subplot(2,1,2)
    histplot(c, d, normalization=%f, style=5);
    xtitle("Non normalized histogram")

d = grand(1000,1,"bin", 6, 0.5); c = linspace(-0.5,6.5,8); clf() subplot(2,1,1) histplot(c, d, style=2) xtitle("normalized histogram") subplot(2,1,2) histplot(c, d, normalization=%f, style=5) xtitle("non normalized histogram")

Example #3: histogram of an exponential random sample

    lambda = 2;
    X = grand(100000,1,"exp", 1/lambda);
    Xmax = max(X);

    clf()
    histplot(40, X, style=2);
    x = linspace(0,max(Xmax),100)';
    plot2d(x,lambda*exp(-lambda*x),strf="000",style=5)
    legend(["exponential random sample histogram" "exact density curve"]);

lambda = 2; X = grand(100000,1,"exp", 1/lambda); Xmax = max(X); clf() histplot(40, X, style=2) x = linspace(0,max(Xmax),100)'; plot2d(x,lambda*exp(-lambda*x),strf="000",style=5) legend(["exponential random sample histogram" "exact density curve"]);

Example #4: the frequency polygon chart and the histogram of a gaussian random sample

    n = 10;
    data = rand(1,1000,"normal");

    clf(); histplot(n, data, style=12, polygon=%t);
    legend(["normalized histogram" "frequency polygon chart"],"lower_caption");

n=10; data=rand(1,1000,"normal"); clf(); histplot(n,data,style=12,polygon=%t); legend(["normalized histogram" "frequency polygon chart"],"lower_caption");

## See also

- histc
- bar3d
- bar
- plot2d
- dsearch

## History

5.5.0 `polygon` option and `cf` output added.