  Pearson's chi-squared test can detect outliers in the data distribution of a
given set of histograms. However, in fields such as demographics (for e.g.
birth years), outliers may be more easily found in terms of the histogram
smoothness where techniques such as Whipple's or Myers' indices handle
successfully only specific anomalies. This paper proposes smoothness outliers
detection among histograms by using the relation between their discrete total
variations (DTV) and their respective sample sizes. This relation is
mathematically derived to be applicable in all cases and simplified by an
accurate linear model. The deviation of the histogram's DTV from the value
predicted by the model is used as the outlier score and the proposed method is
named Total Variation Outlier Recognizer (TVOR). TVOR requires no prior
assumptions about the histograms' samples' distribution, it has no
hyperparameters that require tuning, it is not limited to only specific
patterns, and it is applicable to histograms with the same bins. Each bin can
have an arbitrary interval that can also be unbounded. TVOR finds DTV outliers
easier than Pearson's chi-squared test. In case of distribution outliers, the
opposite holds. TVOR is tested on real census data and it successfully finds
suspicious histograms. The source code is given at
https://github.com/DiscreteTotalVariation/TVOR.
