Distribution

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 sumOfSquaredDeviation fields meaningless.

JSON representation 
{
  "count": string,
  "mean": number,
  "sumOfSquaredDeviation": number,
  "range": {
    object (Range)
  },
  "bucketOptions": {
    object (BucketOptions)
  },
  "bucketCounts": [
    string
  ],
  "exemplars": [
    {
      object (Exemplar)
    }
  ]
}
Fields
count

string (int64 format)

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

number

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

number

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 232, 3rd edition describes Welford's method for accumulating this sum in one pass.

If count is zero then this field must be zero.
range

object (Range)

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

object (BucketOptions)

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

string (int64 format)

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

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

The order of the values in bucketCounts 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 bucketCounts is the count for the overflow bucket (number N-1).
exemplars[]

object (Exemplar)

Must be in increasing order of value field.

Range

The range of the population values.

JSON representation 
{
  "min": number,
  "max": number
}
Fields
min

number

The minimum of the population values.
max

number

The maximum of the population values.

BucketOptions

BucketOptions describes the bucket boundaries used to create a histogram for the distribution. The buckets can be in a linear sequence, an exponential sequence, or each bucket can be specified explicitly. BucketOptions does not include the number of values in each bucket.

A bucket has an inclusive lower bound and exclusive upper bound for the values that are counted for that bucket. The upper bound of a bucket must be strictly greater than the lower bound. The sequence of N buckets for a distribution consists of an underflow bucket (number 0), zero or more finite buckets (number 1 through N - 2) and an overflow bucket (number N - 1). The buckets are contiguous: the lower bound of bucket i (i > 0) is the same as the upper bound of bucket i - 1. The buckets span the whole range of finite values: lower bound of the underflow bucket is -infinity and the upper bound of the overflow bucket is +infinity. The finite buckets are so-called because both bounds are finite.

JSON representation 
{

  // Union field options can be only one of the following:
  "linearBuckets": {
    object (Linear)
  },
  "exponentialBuckets": {
    object (Exponential)
  },
  "explicitBuckets": {
    object (Explicit)
  }
  // End of list of possible types for union field options.
}
Fields
Union field options. Exactly one of these three fields must be set. options can be only one of the following:
linearBuckets

object (Linear)

The linear bucket.
exponentialBuckets

object (Exponential)

The exponential buckets.
explicitBuckets

object (Explicit)

The explicit buckets.

Linear

Specifies a linear sequence of buckets that all have the same width (except overflow and underflow). Each bucket represents a constant absolute uncertainty on the specific value in the bucket.

There are numFiniteBuckets + 2 (= N) buckets. Bucket i has the following boundaries:

Upper bound (0 <= i < N-1): offset + (width * i).

Lower bound (1 <= i < N): offset + (width * (i - 1)).

JSON representation 
{
  "numFiniteBuckets": integer,
  "width": number,
  "offset": number
}
Fields
numFiniteBuckets

integer

Must be greater than 0.
width

number

Must be greater than 0.
offset

number

Lower bound of the first bucket.

Exponential

Specifies an exponential sequence of buckets that have a width that is proportional to the value of the lower bound. Each bucket represents a constant relative uncertainty on a specific value in the bucket.

There are numFiniteBuckets + 2 (= N) buckets. Bucket i has the following boundaries:

Upper bound (0 <= i < N-1): scale * (growthFactor ^ i).

Lower bound (1 <= i < N): scale * (growthFactor ^ (i - 1)).

JSON representation 
{
  "numFiniteBuckets": integer,
  "growthFactor": number,
  "scale": number
}
Fields
numFiniteBuckets

integer

Must be greater than 0.
growthFactor

number

Must be greater than 1.
scale

number

Must be greater than 0.

Explicit

Specifies a set of buckets with arbitrary widths.

There are size(bounds) + 1 (= N) buckets. Bucket i has the following boundaries:

Upper bound (0 <= i < N-1): bounds[i] Lower bound (1 <= i < N); bounds[i - 1]

The bounds field must contain at least one element. If bounds has only one element, then there are no finite buckets, and that single element is the common boundary of the overflow and underflow buckets.

JSON representation 
{
  "bounds": [
    number
  ]
}
Fields
bounds[]

number

The values must be monotonically increasing.

Exemplar

Exemplars are example points that may be used to annotate aggregated distribution values. They are metadata that gives information about a particular value added to a Distribution bucket, such as a trace ID that was active when a value was added. They may contain further information, such as a example values and timestamps, origin, etc.

JSON representation 
{
  "value": number,
  "timestamp": string,
  "attachments": [
    {
      "@type": string,
      field1: ...,
      ...
    }
  ]
}
Fields
value

number

Value of the exemplar point. This value determines to which bucket the exemplar belongs.
timestamp

string (Timestamp format)

The observation (sampling) time of the above value.
attachments[]

object

Contextual information about the example value. Examples are:

Trace: type.googleapis.com/google.monitoring.v3.SpanContext

Literal string: type.googleapis.com/google.protobuf.StringValue

Labels dropped during aggregation: type.googleapis.com/google.monitoring.v3.DroppedLabels

There may be only a single attachment of any given message type in a single exemplar, and this is enforced by the system.