By Uri Bram
The recent, pocket variation of Thinking Statistically comprises all of the fabric from the Kindle unique plus cutting edge new segments giving graphical representations of statistical recommendations. considering Statistically is the e-book that exhibits you the way to imagine like a statistician, with no caring approximately formal statistical recommendations. alongside the way in which we learn the way choice bias can clarify why your boss doesn’t recognize he sucks (even whilst every body else does); tips to use Bayes’ Theorem to make a decision in the event that your associate is dishonest on you; and why Mark Zuckerberg shouldn't ever be used as an instance for whatever. See the area in an entire new mild, and make higher judgements and decisions with out ever going close to a t-test. imagine. imagine Statistically.
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Extra resources for Thinking Statistically
Y = 0, 1, 2, . . 1. 4 μ=1 0 5 10 y 15 20 0 5 10 y 15 20 0 5 10 y 15 20 Fig. 2. 3. There is good agreement of the data with the Poisson model. In the sample there are more women with no children, and fewer with one child, compared to the Poisson model predictions. 5 Negative binomial The classic derivation of the negative binomial distribution is as the number of failures in Bernoulli trials until r successes. Having y failures implies that trial r + y is a success, and in the previous r + y − 1 trials there were exactly r − 1 successes and y failures.
Mathematical derivation. To avoid notational confusion here the mean of the conditional distribution of y is denoted as λ (rather than μ). Given λ, assume the distribution of y is Poisson with mean λ: y | λ ∼ P(λ) ⇒ f (y | λ) = e−λ λy . y! Suppose λ is regarded as a continuous random variable with probability function g(λ) where g(λ) = 0 for λ < 0. Then the unconditional probability function of y is ∞ f (y) = f (y | λ) g(λ) dλ . e. 6): ∞ e−λ λy λ−1 λν e−λν/μ dλ y! Γ (ν) μ 0 ν ∞ ν 1 λy+ν−1 e−λ(1+ν/μ) dλ = y!
This displays linearity and approximate homoskedasticity, and therefore a linear model based on log claims as the response and log accidents as the explanatory variable, is more amenable to analysis using the normal linear model than one based on the raw data. 2. Linear modeling 8 6 0 2 4 Log claims 4000 2000 0 Claims 6000 50 0 2000 4000 6000 8000 3 4 Accidents 5 6 7 8 9 Log accidents 0 0 Frequency 20 40 60 80 Frequency 20 40 60 Fig. 1. Scatterplots of number of accidents and number of claims, raw and log scales 2000 0 2 6000 Accidents 10000 0 2000 4000 Claims 6000 0 0 Frequency 5 10 15 Frequency 5 10 15 20 20 0 4 6 8 Log accidents 10 0 2 4 6 Log claims 8 10 Fig.
Thinking Statistically by Uri Bram