VoseOgive1

See also: VoseOgive2, Ogive distribution, Fitting a continuous non-parametric first-order distribution to data

VoseOgive1()

 

 

Example model

This array function generates a set of "best guess" values for the cumulative probability that correspond to a set of data ranked in increasing order. If there are k data values, then the VoseOgive1() function should span k cells. It will return the values:

1/(k+1)

2/(k+1)

...

k/(k+1)

The data array (let us call them the {xi}) and VoseOgive1 array can then be used to produce an empirical estimate of the cumulative distribution of the parent distribution from which the data come.

See Fitting a continuous non-parametric first-order distribution to data for an explanation about the theory behind this function.

Including second-order uncertainty

The values generated by VoseOgive1() provide us with a "best guess" for the non-parametric distribution. However, the smaller the dataset, the greater the uncertainty about the constructed non-parametric distribution is. We can use the Bayesian technique explained here to take this uncertainty into account.  

To generate an array of the F(xi) values use the VoseOgive2() function. As opposed to VoseOgive1, VoseOgive2 will generate a new array of values on each recalculation.

Constructing the Ogive directly

You can directly construct an Ogive distribution based on min, max and {xi} parameters using the ModelRisk VoseOgive (first-order) and VoseOgiveU (second-order) functions.

 

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