Browse Prior Art Database

HILL-SHAPED DISTRIBUTIONS FOR STATISTICAL APPLICATIONS

IP.com Disclosure Number: IPCOM000009068D
Original Publication Date: 1999-Jun-01
Included in the Prior Art Database: 2002-Aug-06
Document File: 3 page(s) / 135K

Publishing Venue

Motorola

Related People

J. Albert Chiou: AUTHOR

Abstract

To create a probability density function (PDF) and methodology to improve the normal distribution and Weibull distribution for statistical applications.

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MOTOROLA Technical Developments

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HILL-SHAPED DISTRIBUTIONS FOR STATISTICAL APPLICATIONS

by J. Albert Chiou

PURPOSE

  To create a probability density function (PDF) and methodology to improve the normal distribution and Weibull distribution for statistical applications.

BACKGROUND

  The normal distribution or Weibull distribution are used widely for various statistical applications in the industry but they can be improved due to an unrealistic infinite distribution. The normal distrib- ution has a negative infinite random variable and a positive i&mite random variable. The Weibull dis- tribution has a positive infinite random variable. In the real world, the random variable usually has cer- tam limits. Just to name a few examples, the yield strength of G10350 steel at 50 Ksi mean level can not be lower than 0 Ksi or higher than a certain strength level, 500 Ksi or 1000 Ksi for an example The resistivity of copper with a mean value of
1.673e-8 ohm-m at room temperature can not be lower than 0 ohm-m or higher than a certain resistivity number, 0.001 ohm-m for an example.

ADVANTAGES

1. Hill-shaped distribution with a no-infinite-tail approach
2. Use the physical constraints or judged con- straints as the upper bound and lower bound for the distribution.
3. Can assign different PDFs in different random variable ranges
4. Easy to calculate the probability or cumulative distribution function (CDF) due to its linear piecewise fitting.

  This methodology provides a more realistic approach in the real world applications. The PDF distribution is in a physically limited range instead of an infinite range. The calculation of CDF is sim- plified. Users do not have to do complicated inte- gration to predict the probability. Instead, users can easily predict the probability by calculating the trapezoid or triangle (a simplified trapezoid) areas. This concept can be applied in the engineering, science, and liberal arts industries for various statistical applications...