# Schema for Statistics (statistics.json file)
<a name="model-monitor-byoc-statistics"></a>

The schema defined in the `statistics.json` file specifies the statistical parameters to be calculated for the baseline and data that is captured. It also configures the bucket to be used by [KLL](https://datasketches.apache.org/docs/KLL/KLLSketch.html), a very compact quantiles sketch with lazy compaction scheme.

```
{
    "version": 0,
    # dataset level stats
    "dataset": {
        "item_count": number
    },
    # feature level stats
    "features": [
        {
            "name": "feature-name",
            "inferred_type": "Fractional" | "Integral",
            "numerical_statistics": {
                "common": {
                    "num_present": number,
                    "num_missing": number
                },
                "mean": number,
                "sum": number,
                "std_dev": number,
                "min": number,
                "max": number,
                "distribution": {
                    "kll": {
                        "buckets": [
                            {
                                "lower_bound": number,
                                "upper_bound": number,
                                "count": number
                            }
                        ],
                        "sketch": {
                            "parameters": {
                                "c": number,
                                "k": number
                            },
                            "data": [
                                [
                                    num,
                                    num,
                                    num,
                                    num
                                ],
                                [
                                    num,
                                    num
                                ][
                                    num,
                                    num
                                ]
                            ]
                        }#sketch
                    }#KLL
                }#distribution
            }#num_stats
        },
        {
            "name": "feature-name",
            "inferred_type": "String",
            "string_statistics": {
                "common": {
                    "num_present": number,
                    "num_missing": number
                },
                "distinct_count": number,
                "distribution": {
                    "categorical": {
                         "buckets": [
                                {
                                    "value": "string",
                                    "count": number
                                }
                          ]
                     }
                }
            },
            #provision for custom stats
        }
    ]
}
```

**Notes**  
The specified metrics are recognized by SageMaker AI in later visualization changes. The container can emit more metrics if required.
[KLL sketch](https://datasketches.apache.org/docs/KLL/KLLSketch.html) is the recognized sketch. Custom containers can write their own representation, but it won’t be recognized by SageMaker AI in visualizations.
By default, the distribution is materialized in 10 buckets. You can't change this.