Statistics Galton’s Heights of Hypothetical Men (1869)

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Presentation transcript:

Statistics Galton’s Heights of Hypothetical Men (1869)

Statistical Inference

Some Probability Density Functions Normal: outcome influenced by a very large number of very small, ‘50-50 chance’ effects (Ex: human heights) Lognormal: outcome influenced by a very large number of very small, ‘constrained’ effects (Ex: rain drops) Poisson: outcome influenced by a rarely occurring events in a very large population (Ex: micrometeoroid diameters in LEO) Weibull: outcome influenced by a ‘failure’ event in a very large population (Ex: component life time) Binomial: outcome influenced by a finite number of ’50-50 chance’ effects (Ex: coin toss)

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Statistics Using MATLAB ® MATLAB ® ’s statistics toolbox contains distributions such as the normal (norm), Student’s t (t), and  2 (chi2). Some useful command prefixes are the probability density function (pdf), probability distribution function (cdf), and the inverse of the distributions (inv). The command normpdf(x,x',σ) gives the value of p(x). normpdf(0,0,1) = The command normcdf(x *,x',σ) gives normcdf(1,0,1) = (= ) normal error function, p(z 1 ) = normcdf(z 1,0,1) – 0.5 The command norminv(P,x',σ) gives x* from the cdf norminv(0.8413,0,1) = 1

Statistics Using MATLAB ® (cont’d) To obtain the value of z for a given %P, x' and σ: z(95,0,1) = 1.96 and z(95.45,0,1) = 2.00

Degrees of Freedom The number of degrees of freedom,, equal the number of data points, N, minus the number of independent restrictions (constraints), c, used for the required calculations. When computing the sample mean, When computing the sample standard deviation, When constructing a histogram, When performing a regression analysis, where m is the order of the fit (linear, m = 1).