Returns the cumulative distribution function of a distribution evaluated at a specified value. Via mean and standard deviation.

Syntax

=MM_CDF_MS("DistName", X, Mean, [StdDev], [Param3])

• "DistName"
  String. Name of the desired distribution. 

• X
  The value at which the cumulative distribution function is evaluated. 

• Mean
  Mean of the desired distribution. 

• StdDev (optional/required depending on the distribution)
  Standard deviation of the desired distribution. 

• Param3 (optional/required depending on the distribution)
  Third parameter of the distribution.

Remarks

• To check all supported distributions, see MM_DISTRIBUTIONSLIST function. 

• Use MM_CDF to evaluate the cumulative distribution function via distribution parameters.
  Use MM_CDF_TRUNC to evaluate the cumulative distribution function of a truncated distribution (with distribution parameters).
  Use MM_CDF_MS_TRUNC to evaluate the cumulative distribution function of a truncated distribution (with mean and standard deviation). 

• See MM_PDF for probability density function.
  See MM_InvCDF for inverse cumulative distribution function. 

Example 1: Bernoulli distribution

Formula1: =MM_CDF_MS("Bernoulli",0.8,0.85)
Evaluates at 0.8 the cumulative distribution function of a Bernoulli distribution with a mean equal to 0.85. Returns 0.15. Note that this gives the same result as =MM_CDF("Bernoulli", 0.8,0.85) as the mean of the Bernoulli distribution is equal to the probability of success of the Bernoulli trial. 

Formula2: =MM_CDF_MS("Bernoulli", 0.8,0.85,2)
Evaluates at 0.8 the cumulative distribution function of a Bernoulli distribution with a mean equal to 0.85. Returns 0.15. Note that the standard deviation is equal to approximately 0.36 and not 2. As this probability distribution has only one degree of freedom, the StdDev parameter is ignored. 

Example 2: Gamma distribution

Formula3: =MM_CDF_MS("Gamma",1.15,4,8)
Evaluates, at x equal to 1.15, the cumulative distribution function of a Gamma distribution with mean and standard deviation equal to 4 and 8, respectively. Returns approximately 0.56.