# logHist: Plot Log-Histogram In HyperbolicDist: The Hyperbolic Distribution

 logHist R Documentation

## Plot Log-Histogram

### Description

Plots a log-histogram, as in for example Feiller, Flenley and Olbricht (1992).

The intended use of the log-histogram is to examine the fit of a particular density to a set of data, as an alternative to a histogram with a density curve. For this reason, only the log-density histogram is implemented, and it is not possible to obtain a log-frequency histogram.

The log-histogram can be plotted with histogram-like dashed vertical bars, or as points marking the tops of the log-histogram bars, or with both bars and points.

### Usage

```  logHist(x, breaks = "Sturges",
include.lowest = TRUE, right = TRUE,
main = paste("Log-Histogram of", xName),
xlim = range(breaks), ylim = NULL, xlab = xName,
ylab = "Log-density", nclass = NULL, htype = "b", ...)

```

### Arguments

 `x` A vector of values for which the log-histogram is desired. `breaks` One of: a vector giving the breakpoints between log-histogram cells; a single number giving the number of cells for the log-histogram; a character string naming an algorithm to compute the number of cells (see Details); a function to compute the number of cells. In the last three cases the number is a suggestion only. `include.lowest` Logical. If `TRUE`, an ‘x[i]’ equal to the ‘breaks’ value will be included in the first (or last, for `right = FALSE`) bar. `right` Logical. If `TRUE`, the log-histograms cells are right-closed (left open) intervals. `main, xlab, ylab` These arguments to `title` have useful defaults here. `xlim` Sensible default for the range of x values. `ylim` Calculated by `logHist`, see Details. `nclass` Numeric (integer). For compatibility with `hist` only, `nclass` is equivalent to `breaks` for a scalar or character argument. `htype` Type of histogram. Possible types are: '"h"' for a *h*istogram only; '"p"' for *p*oints marking the top of the histogram bars only; '"b"' for *b*oth. `...` Further graphical parameters for calls to `plot` and `points`.

### Details

Uses `hist.default` to determine the cells or classes and calculate counts.

To calculate `ylim` the following procedure is used. The upper end of the range is given by the maximum value of the log-density, plus 25% of the absolute value of the maximum. The lower end of the range is given by the smallest (finite) value of the log-density, less 25% of the difference between the largest and smallest (finite) values of the log-density.

A log-histogram in the form used by Feiller, Flenley and Olbricht (1992) is plotted. See also Barndorff-Nielsen (1977) for use of log-histograms.

### Value

Returns a list with components:

 `breaks` The n+1 cell boundaries (= `breaks` if that was a vector). `counts` n integers; for each cell, the number of `x[]` inside. `logDensity` Log of f^(x[i]), which are estimated density values. If `all(diff(breaks) == 1)`, estimated density values are the relative frequencies `counts/n` and in general satisfy sum[i; f^(x[i]) (b[i+1]-b[i])] = 1, where b[i] = `breaks[i]`. `mids` The n cell midpoints. `xName` A character string with the actual `x` argument name. `heights` The location of the tops of the vertical segments used in drawing the log-histogram. `ylim` The value of `ylim` calculated by `logHist`.

### Author(s)

David Scott d.scott@auckland.ac.nz, Richard Trendall, Thomas Tran

### References

Barndorff-Nielsen, O. (1977) Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. Lond., A353, 401–419.

Barndorff-Nielsen, O. and Bl<e6>sild, P (1983). Hyperbolic distributions. In Encyclopedia of Statistical Sciences, eds., Johnson, N. L., Kotz, S. and Read, C. B., Vol. 3, pp. 700–707. New York: Wiley.

Fieller, N. J., Flenley, E. C. and Olbricht, W. (1992) Statistics of particle size data. Appl. Statist., 41, 127–146.

`hist`

### Examples

```data(SandP500)
### Consider proportional changes in the index
change <- SandP500[-length(SandP500)]/SandP500[-1]
hist(change)
logHist(change)
### Show points only
logHist(change, htype = "p", pch = 20, cex = 0.5)
### Fit the hyperbolic distribution to the changes
hyperbFit(change)
```

HyperbolicDist documentation built on March 18, 2022, 6:23 p.m.