1 / 11

Special Continuous Probability Distribution Lognormal Distribution

PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS. Special Continuous Probability Distribution Lognormal Distribution. f(x). x. 0. Lognormal Distribution – Probability Density Function.

emil
Download Presentation

Special Continuous Probability Distribution Lognormal Distribution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS Special Continuous Probability DistributionLognormal Distribution

  2. f(x) x 0 Lognormal Distribution – Probability Density Function A random variable X is said to have the Lognormal Distribution with parameters  and , where  > 0 and  > 0, if the probability density function of X is: , for X >0 , for X 0 

  3. Lognormal Distribution If X ~ LN(,), then Y= ln (X) ~ N(,)

  4. Lognormal Distribution - Probability Distribution Function where F(z) is the cumulative probability distribution function of N(0,1)

  5. Lognormal Distribution Mean or Expected Value of X Percentile of X Standard Deviation of X

  6. Lognormal Distribution - Example A theoretical justification based on a certain material failure mechanism underlies the assumption that ductile strength X of a material has a lognormal distribution. If the parameters are µ=5 and σ=0.1 , Find: µx and σx P(X >120) P(110 ≤ X ≤ 130) The median ductile strength The expected number having strength at least 120, if ten different samples of an alloy steel of this type were subjected to a strength test. (f) The minimum acceptable strength, If the smallest 5% of strength values were unacceptable.

  7. Lognormal Distribution –Example Solution (a)

  8. Lognormal Distribution –Example Solution (b)

  9. Lognormal Distribution –Example Solution (C) (d)

  10. Lognormal Distribution –Example Solution (e) Let Y=number of items tested that have strength of at least 120 y=0,1,2,…,10

  11. Lognormal Distribution –Example Solution f) The value of x, say xms, for which is determined as follows: and , , so that , therefore

More Related