Histogram bins

Figure 3.3 Hypothetical distribution of dipole moment magnitudes from a simulation of liquid water. The dashed curve is generated by connecting the tops of histogram bins whose height is dictated by the number of water molecules found to have dipole moments in the range spanned by the bin. Note that although the example is illustrated to be symmetric about a central value (which will thus necessarily be (/z)) this need not be the case...

Probability density functions, or histograms, of the product of instantaneous temperature x velocity were obtained through use of this combustion probe system for a variety of downsteam and radial flame test positions. A typical histogram is shown in Fig. 3, while Fig. 4 displays the same data (as well as data for a test position further downsteam) in a "scattergram" format i.e., in a plot of velocity vs. temperature. Here, each datum corresponds to a specific shot, while the histogram bins correspond to integrated results from numbers of shots. 

Lbinr number of histogram bins used for the pilot sample value... 

Figure 8.26. The matricized arrays of the peat example (35 x 21) shown as images the data, the model and the absolute value of the residual. The greyvalues represent the lengths of histogram bars in the 2D histogram. The horizontal axis represents the 21 particle area histogram bins, the vertical axis shows the five peat types x seven treatments.

Wand, M.P. Data-based choice of histogram bin width. American Statistician 1997 51 59-64. 

The expected value recorded in the histograms bin corresponding to energy... 

Fig. 14 Schematic construction of a scatter diagram image A (top left) image B (bottom left) scatter diagram (right). The pixels at location (205,37) have intensities 41 and 21, respectively, and therefore, histogram bin (41,21) is incremented.

For each histogram bin thus defined, a statistical counting error can be assigned as described below. 

The first approximation that is made for this description is that B = 0 that is, that there is no time-independent background of events unrelated to muon decay. Since experimental values of B are usually less than a few percent, this is a tolerable approximation, especially for early times. The raw histogram bins can therefore be represented as... 

Figure 5.5 Distribution of score values calculated for 218 screening experiments. The shading and the percentage values show how many of the experiments gave co-crystals within each histogram bin.

Figure 13.5 also shows the experimental [67] and simulated transmission electron microscopy images (TEM) of MCM-41. The relative intensity A/// of each histogram point is calculated by applying the Beer-Lambert law to each histogram bin ... 

Here p is the estimated probability, or frequency, of the occurrence of a specific channel of data. The pi corresponds to a particular histogram bin count normalized by the sum of all bin counts, c, being the bin count for a particular bin (Eq. [2]) ... 

As stated, the reason for formulating the SSE is to remove the dependence of the entropy metric on the number of histogram bins. However,... 

M. P. Wand, /. Am. Stat. Assoc., 85, 59 (1997). Data-based Choice of Histogram Bin Width. 

Fig. 4 Distribution of 1,312 lithium oxides extracted from the ICSD database with respect to fractional accessible volume of the crystal structure space with bond valence mismatch of less than 0.2 valence units. The histogram bin size is 0.001. According to Avdeev et al. [10], structures with high values of the fractional accessible volume per ion of the mobile species may be expected to have high ionic conductivity...

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