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# Histogram Analysis

In statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable.

Histograms are used to plot density of data, and often for density estimation: estimating the probability density function of the underlying variable. In a more general mathematical sense, a histogram is a function mi that counts the number of observations that fall into each of the disjoint categories (known as bins), whereas the graph of a histogram is merely one way to represent a histogram.

Thus, if we let n be the total number of observations and k be the total number of bins, the histogram mi meets the following conditions:

A cumulative histogram is a mapping that counts the cumulative number of observations in all of the bins up to the specified bin:

## Remarks

- An alternative to the histogram is kernel density estimation, which uses a kernel to smooth samples. This will construct a smooth probability density function, which will in general more accurately reflect the underlying variable.
- The histogram provides important information about the shape of a distribution. According to the values presented, the histogram is either highly or moderately skewed to the left or right. A symmetrical shape is also possible, although a histogram is never perfectly symmetrical. If the histogram is skewed to the left, or negatively skewed, the tail extends further to the left.

## Examples

## References

- Balakrishnan, N., Exponential Distribution: Theory, Methods and Applications, CRC, P 18 1996.