page_title: Cumulative frequency analysis
section_title: Histogram
hierarchical_section_title: Cumulative frequency analysis / Histogram
caption_attribution_description: English: Histogram of yield of wheat. Data from O.P.Singh on sample plot data in farmers' fields, Gohana, Haryana, India
context_page_description: Cumulative frequency analysis is the analysis of the frequency of occurrence of values of a phenomenon less than a reference value. The phenomenon may be time- or space-dependent. Cumulative frequency is also called frequency of non-exceedance.
  Cumulative frequency analysis is performed to obtain insight into how often a certain phenomenon is below a certain value. This may help in describing or explaining a situation in which the phenomenon is involved, or in planning interventions, for example in flood protection.
  This statistical technique can be used to see how likely an event like a flood is going to happen again in the future, based on how often it happened in the past. It can be adapted to bring in things like climate change causing wetter winters and drier summers.
context_section_description: The observed data can be arranged in classes or groups with serial number k. Each group has a lower limit (Lₖ) and an upper limit (Uₖ). When the class (k) contains mₖ data and the total number of data is N, then the relative class or group frequency is found from:
  Fg(Lₖ < X ≤ Uₖ)  = mₖ / N
  or briefly:
  Fgₖ = m/N
  or in percentage:
  Fg(%) = 100m/N
  The presentation of all class frequencies gives a frequency distribution, or histogram. Histograms, even when made from the same record, are different for different class limits.
  The histogram can also be derived from the fitted cumulative probability distribution:
  Pgₖ = Pc(Uₖ) − Pc(Lₖ)
  There may be a difference between Fgₖ and Pgₖ due to the deviations of the observed data from the fitted distribution (see blue figure).
  Often it is desired to combine the histogram with a probability density function as depicted in the black and white picture.
caption: Histogram derived from the adapted cumulative probability distribution
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