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Maths Probability Function

Calculate normal and log normal probability density, cumulative distribution function and complementary distribution function from the mean, standard deviation and percentile.

The cumulative probability can be calculated from the percentile, or the percentile can be calculated from the cumulative probability. The cumulative distribution (cdf) function asymptotes to 1 as the percentile tends to infinity. The complementary distribution function asymptotes to 0 as the percentile x tends to infinity. Use the Result Plot option to plot the probability density, cumulative distribution, and complementary distribution (or tail) versus the percentile.

Reference : Numerical Recipes, The Art Of Scientific Computing, Press, Teukolsky, Vetterling, Flannery, Cambridge University Press

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CALCULATOR : Normal Probability Distribution [FREE]   ±

Calculate the normal probability density, cumulative distribution function and complementary distribution function from the mean, standard deviation and percentile.

The cumulative probability can be calculated from the percentile, or the percentile can be calculated from the cumulative probability. The cumulative distribution (cdf) function asymptotes to 1 as the percentile tends to infinity. The complementary distribution function asymptotes to 0 as the percentile x tends to infinity. Use the Result Plot option to plot the probability density, cumulative distribution, and complementary distribution (or tail) versus the percentile.

Tool Input

  • pxtype : Probability Type
    • xu : User Defined Percentile
    • pu : User Defined Cumulative Probability
  • m : Mean Value
  • s : Standard Deviation

Tool Output

  • d : Probability Density
  • p : Cumulative Probability
  • q : Tail Probability Or Exceedance
  • x : Percentile

CALCULATOR : Log Normal Probability Distribution [FREE]   ±

Calculate the log normal probability density, cumulative distribution function and complementary distribution function from the mean, standard deviation and percentile.

The cumulative probability can be calculated from the percentile, or the percentile can be calculated from the cumulative probability. The arithmetic mean, arithmetic standard deviation, median and mode are also calculated. The cumulative distribution (cdf) function asymptotes to 1 as the percentile tends to infinity. The complementary distribution function asymptotes to 0 as the percentile x tends to infinity. Use the Result Plot option to plot the probability density, cumulative distribution, and complementary distribution (or tail) versus the percentile.

Tool Input

  • pxtype : Probability Type
    • xu : User Defined Percentile
    • pu : User Defined Cumulative Probability
  • m : Mean Value
  • s : Standard Deviation

Tool Output

  • am : Arithmetic Mean
  • as : Arithmetic Standard Deviation
  • d : Probability Density
  • med : Median
  • mod : Mode
  • p : Cumulative Probability
  • q : Tail Probability Or Exceedance
  • x : Percentile