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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
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
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
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
T. R. Willemain MAU Spring 06 9 Lognormal

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T. R. Willemain MAU Spring 06 10 Lognormal
T. R. Willemain MAU Spring 06 11 Weibull

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T. R. Willemain MAU Spring 06 12 Weibull
T. R. Willemain MAU Spring 06 13

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T. R. Willemain MAU Spring 06 14 Gamma
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.
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
T. R. Willemain MAU Spring 06

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Class 04 Continuous probability models - Models of...

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