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# Realistic Distribution for Monte Carlo Simulation

IP.com Disclosure Number: IPCOM000101968D
Original Publication Date: 1990-Sep-01
Included in the Prior Art Database: 2005-Mar-17
Document File: 2 page(s) / 66K

IBM

## Related People

Arthurson, D: AUTHOR [+2]

## Abstract

An algorithm for generating a novel type of skewed distribution in which both the skew and the magnitude of the variation can be controlled.

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Realistic Distribution for

Monte Carlo

Simulation

An algorithm for generating a novel type of skewed
distribution in which both the skew and the magnitude of the
variation can be controlled.

A Monte Carlo simulation process requires a distributed set of
values on which to work.  There are many such distributions, straight
lines, polynominal curves, standard distributions and so on.  One
very common one is a normal distribution which occurs frequently in
nature but infrequently in business.  Disclosed is a new variation on
a normal distribution curve and how values on such a curve can be
computed.

A normal distribution curve, when referring to probabilities,
states that values on either side of the mean are equally likely and
that the distribution of the magnitudes of the values on either side
of the normal are the same.  So the curve is symmetrical.  This kind
of distribution is unsuitable for many business needs. Consider, for
example, price changes to a product.  Attempts to simulate possible
price changes using a normal distribution say two things:  firstly,
that a price is as likely to increase as it is to decrease and,
secondly, that the range of values that the price could be, if it
increases is the same as the range that it could be if it decreases.
Neither of these situations is likely to occur in practice.

Needed therefore is some kind of skewed distribution that
reflects what is believed will really happen.  That is, prices are
more likely to rise than they are to decrease; also that when they
rise, they are likely to rise by a large amount but when they
decrease, the decrease will be small. A standard skewed distribution
does not do this - it only allows the rise to be more likely than
the decrease and does not affect the magnitude of the variation.

A new kind of modified skewed distribution is described that
allows both elements to vary to match reality.  It is called
'proportional distribution.'  Also included is a method for producing
values that lie on this distribution so tha...