Continuous Unbounded Kernel distribution | Vose Software

Continuous Unbounded Kernel distribution

Format: KernelCU({data})

The KernelCU distribution is a kernel estimated distribution based on a set of data, assuming the variable is continuous (C) and unbounded (U).


The KernelCU function can be used to estimate the population distribution from a set of random observations {data} when it is known that the variable is continuous and unbounded. ModelRisk also offers the Ogive distribution for this purpose, but with that distribution one must specify a minimum and maximum.


The KernelCU distribution was first developed as a simulation tool by the risk analyst, David Vose.

The KernelCU is constructed by wrapping a Normal distribution around each value in {data} and then taking the average of all the distributions’ densities. The mean of each Normal distribution is the observed value in question, the standard deviation is given by:


where n is the number of observations and s is the standard deviation of the data.

ModelRisk functions added to Microsoft Excel for the Continuous Unbounded Kernel distribution

VoseKernelCU generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseKernelCUObject constructs a distribution object for this distribution.

VoseKernelCUProb returns the probability density or cumulative distribution function for this distribution.

VoseKernelCUProb10 returns the log10 of the probability density or cumulative distribution function.


Continuous Unbounded Kernel distribution equations