cumulant

(noun)

Any of a set of parameters of a one-dimensional probability distribution of a certain form.

Related Terms

  • empirical rule
  • entropy

Examples of cumulant in the following topics:

  • Cumulative Frequency Distributions

    • A cumulative frequency distribution displays a running total of all the preceding frequencies in a frequency distribution.
    • A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.
    • The third column should be labeled Cumulative Frequency.
    • There are a number of ways in which cumulative frequency distributions can be displayed graphically.
    • This image shows the difference between an ordinary histogram and a cumulative frequency histogram.
  • Frequency Polygons

    • Frequency polygons are also a good choice for displaying cumulative frequency distributions.
    • A cumulative frequency polygon for the same test scores is shown in Figure 2.
    • Since 642 students took the test, the cumulative frequency for the last interval is 642.
    • It is also possible to plot two cumulative frequency distributions in the same graph.
  • Relative Frequency Distributions

    • Just like we use cumulative frequency distributions when discussing simple frequency distributions, we often use cumulative frequency distributions when dealing with relative frequency as well.
    • Cumulative relative frequency (also called an ogive) is the accumulation of the previous relative frequencies.
    • To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.
  • Frequency

    • Cumulative relative frequency is the accumulation of the previous relative frequencies.
    • To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.
    • The last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated.
    • This percentage is the cumulative relative frequency entry in the third row.
    • To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row.
  • Continuous Probability Distributions

    • Mathematicians also call such a distribution "absolutely continuous," since its cumulative distribution function is absolutely continuous with respect to the Lebesgue measure $\lambda$.
    • The definition states that a continuous probability distribution must possess a density; or equivalently, its cumulative distribution function be absolutely continuous.
    • This requirement is stronger than simple continuity of the cumulative distribution function, and there is a special class of distributions—singular distributions, which are neither continuous nor discrete nor a mixture of those.
  • Optional Collaborative Classrom Exercise

    • In your class, have someone conduct a survey of the number of siblings (brothers and sisters) each student has.Create a frequency table.Add to it a relative frequency column and a cumulative relative frequency column.Answer the following questions:
  • Summary

  • Properties of Continuous Probability Distributions

    • Area under the curve is given by a different function called the cumulative distribution function (abbreviated: cdf).
    • The cumulative distribution function is used to evaluate probability as area.
  • Practice 1: Goodness-of-Fit Test

    • The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as follows: (Source: HIV/AIDS Epidemiology Santa Clara County, Santa Clara County Public Health Department, May 2011)
  • Determining Sample Size

    • As follows, this can be estimated by pre-determined tables for certain values, by Mead's resource equation, or, more generally, by the cumulative distribution function.
    • Calculate the appropriate sample size required to yield a certain power for a hypothesis test by using predetermined tables, Mead's resource equation or the cumulative distribution function.
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