Class Distribution (2.2.0)

Distribution contains summary statistics for a population of values. It optionally contains a histogram representing the distribution of those values across a set of buckets.

The summary statistics are the count, mean, sum of the squared deviation from the mean, the minimum, and the maximum of the set of population of values. The histogram is based on a sequence of buckets and gives a count of values that fall into each bucket. The boundaries of the buckets are given either explicitly or by formulas for buckets of fixed or exponentially increasing widths.

Although it is not forbidden, it is generally a bad idea to include non-finite values (infinities or NaNs) in the population of values, as this will render the mean and sum_of_squared_deviation fields meaningless.

Field number for the "bucket_counts" field.

Field number for the "bucket_options" field.

Field number for the "count" field.

Field number for the "exemplars" field.

Field number for the "mean" field.

Field number for the "range" field.

Field number for the "sum_of_squared_deviation" field.

The number of values in each bucket of the histogram, as described in bucket_options . If the distribution does not have a histogram, then omit this field. If there is a histogram, then the sum of the values in bucket_counts must equal the value in the count field of the distribution.

If present, bucket_counts should contain N values, where N is the number of buckets specified in bucket_options . If you supply fewer than N values, the remaining values are assumed to be 0.

The order of the values in bucket_counts follows the bucket numbering schemes described for the three bucket types. The first value must be the count for the underflow bucket (number 0). The next N-2 values are the counts for the finite buckets (number 1 through N-2). The N'th value in bucket_counts is the count for the overflow bucket (number N-1).

Defines the histogram bucket boundaries. If the distribution does not contain a histogram, then omit this field.

The number of values in the population. Must be non-negative. This value must equal the sum of the values in bucket_counts if a histogram is provided.

Must be in increasing order of value field.

The arithmetic mean of the values in the population. If count is zero then this field must be zero.

If specified, contains the range of the population values. The field must not be present if the count is zero.

The sum of squared deviations from the mean of the values in the population. For values x_i this is:

Sum[i=1..n]((x_i - mean)^2)

Knuth, "The Art of Computer Programming", Vol. 2, page 323, 3rd edition describes Welford's method for accumulating this sum in one pass.

If count is zero then this field must be zero.