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MEGN 537 – Probabilistic Biomechanics Ch.4 – Common Probability Distributions

MEGN 537 – Probabilistic Biomechanics Ch.4 – Common Probability Distributions. Anthony J Petrella, PhD. Continuous Data. Normal Distribution - infinity to + infinity Lognormal Distribution 0 to + infinity. Beta Distribution. Bounded: where B( a , b ) is the “beta function”.

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MEGN 537 – Probabilistic Biomechanics Ch.4 – Common Probability Distributions

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  1. MEGN 537 – Probabilistic BiomechanicsCh.4 – Common Probability Distributions Anthony J Petrella, PhD

  2. Continuous Data • Normal Distribution - infinity to + infinity • Lognormal Distribution 0 to + infinity

  3. Beta Distribution • Bounded: where B(a,b) is the “beta function” CDF PDF X X Images: http://en.wikipedia.org/wiki/Beta_distribution

  4. Truncated Normal • PDF: where is the PDF of the normal curve, and is the CDF of the normal curve • Applicable for toleranceranges on dimensions

  5. Uniform Distribution • PDF: • Applicable for tolerance rangeson dimensions, temporalvariations PDF L U CDF 1.0 L U

  6. Mean and COV • Expressions for E(X) and COV(X) for different distributions

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