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3. Introductory Examples (Jan10)

# 3. Introductory Examples (Jan10) - Introductory Examples...

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Unformatted text preview: Introductory Examples Rice, Section 10.2, page 378, gives a data set of the melting point of beeswax. This data is in the file Chapter 10, beeswax.txt. Figure 1 gives a relative frequency histogram of the data. The histogram has the general shape of a normal distribution. Consider the family of probability density functions (pdf)’s F = { f : f ( x ; μ,σ 2 ) = 1 √ 2 πσ 2 e- ( x- μ ) 2 2 σ 2 where μ ∈ R,σ 2 > } This is a family of distributions, with parameter space Θ = { ( μ,σ 2 ) : μ ∈ R,σ 2 > } . Thus for an appropriate choice of some f ∈ F , or equivalently an appropriate choice of μ,σ 2 in the parameter space, one can obtain a good description or fit of the data with this particular distribution. Figure 1 is produced using the R program in the file bees.r M e l t i n g P o i n t o f B e e s w a x t e m p Density 6 3 . 0 6 3 . 5 6 4 . 0 6 4 . 5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Figure 1: Beeswax Melting Point with Normal Overlay. Another example of parametric modeling is the modeling of Illinois rainfall data. This data is described in Rice, page 414, problem 42. In this handout the rainfall from the 5 years is combined into one data set. Figure 2 gives a histogram of this data. Overlaid on the histogram is a fitted Gamma distribution....
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3. Introductory Examples (Jan10) - Introductory Examples...

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