histc

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)

h

• If normalization is %T: Probability densities on the bins defined by n or x, such that the bins areas are proportionnal to their populations.

• If normalization is %F: Numbers of elements in the bins.

normalization

scalar boolean (default = %T), setting the type of output (see h).

Description

This function computes 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 "normalized" is selected and else, simply equal to Ni. When normalization occurs the histogram verifies:

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

Examples

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

  // The gaussian random sample
  d = rand(1, 10000, 'normal');
  
  h = histc(20, d, normalization=%f);
  sum(h)   // = 10000
  // We use histplot to show a graphic representation
  clf(); histplot(20, d, normalization=%f);
  
  // Normalized histogram (probability density)
  h = histc(20, d);
  dx = (max(d)-min(d))/20;  sum(h)*dx   // = 1
  clf(); histplot(20, d);

  
• 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)
  h = histc(c, d);
  histplot(c, d, style=2);
  xtitle(_("Normalized histogram"))
  
  subplot(2,1,2)
  h = histc(c, d, normalization=%f);
  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);
  h = histc(40, 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");
  h = histc(n, data);
  
  clf(), histplot(n, data, style=12, polygon=%t);
  legend([_("normalized histogram") _("frequency polygon chart")], "lower_caption");

  

See also

• histplot — esboça um histograma
• hist3d — representação 3d de um histograma
• plot2d — 2D plot
• dsearch — Busca binária (também conhecida como busca dicótoma em francês)

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