cumulant

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.

• Calculating the Payback Period

  • Then Cumulative Cash Flow = (Net Cash Flow Year 1 + Net Cash Flow Year 2 + Net Cash Flow Year 3 ... etc.)
  • Accumulate by year until Cumulative Cash Flow is a positive number: that year is the payback year.
  • Then the cumulative positive cash flows are determined for each period.
  • The modified payback period is calculated as the moment in which the cumulative positive cash flow exceeds the total cash outflow.
  • The modified payback period is in year 5, since the cumulative positive cash flows (17000) exceeds the total cash outflows (12000) in year 5.

• Provisions of Preferred Stock

  • Preferred shares have numerous rights which can be attached to them, such as cumulative dividends, convertibility, and participation.
  • One of these rights may be the right to cumulative dividends.
  • Preferred stock shareholders already have rights to dividends before common stock shareholders, but cumulative preferred shares contain the provision that should a company fail to pay out dividends at any time at the stated rate, then the issuer will have to make up for it as time goes on.

• Convertible Stock

  • The shares may also be cumulative or non-cumulative.
  • A cumulative preferred stock accumulates unpaid prior period dividends into the future, while a non-cumulative preferred loses rights to any dividends not paid in prior periods.

• Accounting for Preferred Stock

  • Cumulative preferred stock is preferred stock for which the right to receive a basic dividend, usually each quarter, accumulates if the dividend is not paid.
  • Companies must pay unpaid cumulative preferred dividends before paying any dividends on the common stock.
  • Dividends in arrears are cumulative unpaid dividends, including the quarterly dividends not declared for the current year.
  • Also, the cumulative dividend for the current year is payable.
  • Differentiate between preferred to dividends, noncumulative, cumulative and convertible preferred stock

• 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 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.

• 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.

• Defining the Payback Method

  • Then cumulative cash flow = (net cash flow year one + net cash flow year two + net cash flow year three).
  • Accumulate by year until cumulative cash flow is a positive number, which will be the payback year.