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Manuscript Title: From Data to Probability Densities without Hostograms
Authors: Bernd A. Berg, Robert C. Harris
Program title: cdf_to_pd
Catalogue identifier: AEBC_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 179(2008)443
Programming language: Fortran 77.
Computer: Any capable of compiling and executing Fortran code.
Operating system: Any capable of compiling and executing Fortran code.
Keywords: Display of data, Probability densities, Histograms, Continuous variables, Cumulative distribution functions.
Classification: 4.14, 9.

Nature of problem:
When one deals with data drawn from continuous variables, a histogram is often inadequate to display the probability density. It deals inefficiently with statistical noise, and binsizes are free parameters. In contrast to that, the empirical cumulative distribution function (obtained after sorting the data) is parameter free. But it is a step function, so that its differentiation does not give a smooth probability density.

Solution method:
Based on Fourier series expansion and Kolmogorov tests, we introduce a simple method, which overcomes this problem. Error bars on the estimated probability density are calculated using a jackknife method. Several examples are included in the distribution file.

Running time:
The test runs provided take only a few seconds to execute.