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).

## Uses

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.