Class 04 Continuous probability models

Class 04 Continuous probability models - Models of...

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T. R. Willemain MAU Spring 06 1 Models of continuous random variables
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T. R. Willemain MAU Spring 06 2 Flashback
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T. R. Willemain MAU Spring 06 3 Agenda Frequently used models of continuous random variables Probability plots for matching models to data In-class exercises Microquiz 04
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T. R. Willemain MAU Spring 06 4 A gallery of continuous probability distributions. Source: NIST
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T. R. Willemain MAU Spring 06 5 Frequently used models Normal can be positive or negative; symmetric; often a good model of measurement error; Central Limit Theorem Lognormal only positive values; logs of these are normal; often a good model of sizes of things Weibull only positive values; often used to model lifetimes Gamma only positive values; often used to model times to complete operations
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T. R. Willemain MAU Spring 06 6 Normal
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T. R. Willemain MAU Spring 06 7 Transformation Given X with known mean and variance, what are the mean and variance of Y = a + b*X
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T. R. Willemain MAU Spring 06 8 Normal
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T. R. Willemain MAU Spring 06 9 Lognormal
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T. R. Willemain MAU Spring 06 10 Lognormal
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T. R. Willemain MAU Spring 06 11 Weibull
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T. R. Willemain MAU Spring 06 12 Weibull
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T. R. Willemain MAU Spring 06 13
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T. R. Willemain MAU Spring 06 14 Gamma
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T. R. Willemain MAU Spring 06 15 Gamma
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T. R. Willemain MAU Spring 06 16 Probability plots Goal is to get a quick graphical confirmation that a given probability model is a reasonable way to describe the distribution of the values of a random variable. Several types of these plots exist. Minitab’s version warps the vertical scale of the empirical CDF plot so that the data plot along a straight line if the model is reasonable.
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T. R. Willemain MAU Spring 06 17
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T. R. Willemain MAU Spring 06 18 C1 Percent 3 2 1 0 -1 -2 -3 99 95 90 80 70 60 50 40 30 20 10 5 1 Probability Plot of C1 Normal - 95% CI
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T. R. Willemain MAU Spring 06
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This note was uploaded on 04/14/2009 for the course ENGR MAU taught by Professor Malaviya during the Spring '09 term at Rensselaer Polytechnic Institute.

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Class 04 Continuous probability models - Models of...

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